Fundamentals Of Corporate Finance 10Th Canadian Edition By Ross - Test Bank

Fundamentals Of Corporate Finance 10Th Canadian Edition By Ross – Test Bank

Instant Download – Complete Test Bank With Answers

Sample Questions Are Posted Below

Chapter 05

Introduction to Valuation: The Time Value of Money

True / False Questions

Jamie deposits $1,000 into an account that pays 4% interest compounded annually. Chris deposits $1,000 into an account that pays 4% simple interest. Both deposits were made today. At the end of five years, Chris will have more money in his account than Jamie has in hers.
FALSE

Accessibility: Keyboard Navigation
Blooms: Understand
Difficulty: Hard
Learning Objective: 05-01 How to determine the future value of an investment made today.
Topic: 05-01 Future Value and Compounding
Topic: 05-03 Investing for More than One Period

Jamie deposits $1,000 into an account that pays 4% interest compounded annually. Chris deposits $1,000 into an account that pays 4% simple interest. Both deposits were made today. At the end of one year, both Jamie and Chris will have the same amount in their accounts.
TRUE

Jamie deposits $1,000 into an account that pays 4% interest compounded annually. Chris deposits $1,000 into an account that pays 4% simple interest. Both deposits were made today. Chris will never earn any interest on interest.
TRUE

Future value can be lower than present value
TRUE

Future value is always higher than present value
FALSE

Tom and Antonio both want to open savings accounts today. Tom wants to have $1,000 in his savings account six years from now. Antonio wants to have $1,000 in his savings account three years from now. Tom needs to deposit more money into his account today than does Antonio.
FALSE

Tom and Antonio both want to open savings accounts today. Tom wants to have $1,000 in his savings account six years from now. Antonio wants to have $1,000 in his savings account three years from now. Tom will need to deposit twice the amount of money today as Antonio.
FALSE

Tom and Antonio both want to open savings accounts today. Tom wants to have $1,000 in his savings account six years from now. Antonio wants to have $1,000 in his savings account three years from now. Antonio needs to deposit more money into his account today than does Tom.
TRUE

As the discount rate increases, the future value of $500 to be received four years from now will decrease:
FALSE

Accessibility: Keyboard Navigation
Blooms: Understand
Difficulty: Easy
Learning Objective: 05-01 How to determine the future value of an investment made today.
Topic: 05-01 Future Value and Compounding
Topic: 05-02 Investing for a Single Period
Topic: 05-03 Investing for More than One Period

The future value will increase the higher the rate of interest.
TRUE

The future value will increase the longer the period of time.
TRUE

The future value will increase the lower the rate of interest.
FALSE

The future value will increase the shorter the period of time.
FALSE

Interest earned on the reinvestment of previous interest payments is called simple interest.
FALSE

Accessibility: Keyboard Navigation
Blooms: Remember
Difficulty: Easy
Learning Objective: 05-01 How to determine the future value of an investment made today.
Topic: 05-03 Investing for More than One Period
Topic: 05-04 A Note on Compound Growth

Jamie deposits $1,000 into an account that pays 4% interest compounded annually. Chris deposits $1,000 into an account that pays 4% simple interest. Both deposits were made today. All else equal, Jamie made the better investment.
TRUE

Accessibility: Keyboard Navigation
Blooms: Understand
Difficulty: Easy
Learning Objective: 05-01 How to determine the future value of an investment made today.
Topic: 05-03 Investing for More than One Period

Present values increase as the discount rate increases.
FALSE

Accessibility: Keyboard Navigation
Blooms: Remember
Difficulty: Medium
Learning Objective: 05-02 How to determine the present value of cash to be received at a future date.
Topic: 05-05 Present Value and Discounting
Topic: 05-06 The Single-Period Case
Topic: 05-07 Present Values for Multiple Periods

Present values increase the further away in time the future value.
FALSE

The higher the discount rate, the higher the present value.
FALSE

Given a constant discount rate, the larger the future value, the larger the present value
TRUE

The larger the present value factor, the larger the present value.
TRUE

The longer the time period, the higher the present value.
FALSE

Compounding is the process of finding the present value of some future amount.
FALSE

Accessibility: Keyboard Navigation
Blooms: Remember
Difficulty: Easy
Learning Objective: 05-02 How to determine the present value of cash to be received at a future date.
Topic: 05-05 Present Value and Discounting
Topic: 05-06 The Single-Period Case
Topic: 05-07 Present Values for Multiple Periods

Discount rate is the interest rate used to calculate the present value of future cash flows.
TRUE

Discounting is the process of finding the present value of some future amount.
TRUE

If the rate at which you can invest is 0%, the value today of $1 to be received in the future is less than $1.
FALSE

Accessibility: Keyboard Navigation
Blooms: Understand
Difficulty: Easy
Learning Objective: 05-02 How to determine the present value of cash to be received at a future date.
Topic: 05-05 Present Value and Discounting
Topic: 05-06 The Single-Period Case
Topic: 05-07 Present Values for Multiple Periods

Present value is the value today of future cash flows discounted at the appropriate discount rate.
TRUE

Present values are always smaller than future values when both r and t are positive
TRUE

The present value will increase the higher the rate of interest.
FALSE

The present value will increase the lower the rate of interest.
TRUE

The I.C. James Co. invested $10,000 six years ago at 5% simple interest. The I.M. Smart Co. invested $10,000 six years ago at 5% interest which is compounded annually. The I.C. James Co. will have an account value of $13,400.96 six years from now.
FALSE

Accessibility: Keyboard Navigation
Blooms: Understand
Difficulty: Hard
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-08 More on Present and Future Values
Topic: 05-09 Present versus Future Value

The I.C. James Co. invested $10,000 six years ago at 5% simple interest. The I.M. Smart Co. invested $10,000 six years ago at 5% interest which is compounded annually. The I.M Smart Co. will earn $525 interest in the second year.
TRUE

The I.C. James Co. invested $10,000 six years ago at 5% simple interest. The I.M. Smart Co. invested $10,000 six years ago at 5% interest which is compounded annually. Both the I.C. James Co. and the I.M. Smart Co. will earn $500 interest in the first year.
TRUE

The future value of a single sum will increase more rapidly when the interest rate increases.
TRUE

Accessibility: Keyboard Navigation
Blooms: Remember
Difficulty: Medium
Learning Objective: 05-01 How to determine the future value of an investment made today.
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-01 Future Value and Compounding
Topic: 05-08 More on Present and Future Values
Topic: 05-09 Present versus Future Value

The future value of a single sum will increase more rapidly when the interest rate decreases.
FALSE

The future value of a single sum will increase more rapidly when the frequency of compounding increases.
TRUE

The future value of a single sum will increase more rapidly when the frequency of compounding decreases.
FALSE

Tom and Antonio both want to open savings accounts today. Tom wants to have $1,000 in his savings account six years from now. Antonio wants to have $1,000 in his savings account three years from now. Antonio needs to deposit twice the amount of money today as Tom.
FALSE

Accessibility: Keyboard Navigation
Blooms: Understand
Difficulty: Medium
Learning Objective: 05-01 How to determine the future value of an investment made today.
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-01 Future Value and Compounding
Topic: 05-08 More on Present and Future Values
Topic: 05-09 Present versus Future Value

Multiple Choice Questions

Marie needs $26,000 as a down payment for a house 4 years from now. She earns 5.25% on her savings. Marie can either deposit one lump sum today for this purpose or she can wait a year and deposit a lump sum. How much additional money must Marie deposit if she waits for one year rather than making the deposit today?
A.$878.98
B. $911.13
C. $1,112.36
D. $1,348.03
E. $1,420.18

Courtney invests $1,200 today. If she can earn a 13.25% rate of return for the next two years, how much money will she have at the end of the two years?
A.$1,203.18
B. $1,232.01
C. $1,359.00
D. $1,539.07
E. $1,742.99

Accessibility: Keyboard Navigation
Blooms: Apply
Difficulty: Easy
Learning Objective: 05-01 How to determine the future value of an investment made today.
Topic: 05-01 Future Value and Compounding
Topic: 05-02 Investing for a Single Period
Topic: 05-03 Investing for More than One Period

If you leave the money of $950 in the account for five years and the account earns 8% compounded annually, what will the balance in the account grow to?
A.$1,341.05
B. $1,347.82
C. $1,395.86
D. $1,406.23
E. $1,491.15

You are supposed to receive $2,000 five years from now. At an interest rate of 6%, what is that $2,000 worth today?
A.$1,491.97
B. $1,492.43
C. $1,494.52
D. $1,497.91
E. $1,499.01

Accessibility: Keyboard Navigation
Blooms: Apply
Difficulty: Easy
Learning Objective: 05-02 How to determine the present value of cash to be received at a future date.
Topic: 05-05 Present Value and Discounting
Topic: 05-06 The Single-Period Case
Topic: 05-07 Present Values for Multiple Periods

You just received $278,000 from an insurance settlement. You have decided to set this money aside and invest it for your retirement. Currently, your goal is to retire 38 years from today. How much more will you have in your account on the day you retire if you can earn an average return of 9.5% rather than just 9.0%?
A.$794,014
B. $1,396,036
C. $1,611,408
D. $1,818,342
E. $2,033,333

Dale invests $500 in an account that pays 6% simple interest. How much more could he have earned over a thirty year period if the interest had compounded annually?
A.$1,471.75
B. $1,532.50
C. $1,621.25
D. $1,804.25
E. $2,371.75

Accessibility: Keyboard Navigation
Blooms: Apply
Difficulty: Easy
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-08 More on Present and Future Values
Topic: 05-09 Present versus Future Value

You collect model cars. One particular model increases in value at a rate of 5% per year. Today, the model is worth $29.50. How much additional money can you make if you wait ten years to sell the model rather than selling it five years from now?
A.$9.98
B. $10.40
C. $10.86
D. $11.03
E. $11.24

An account was opened with $1,000 ten years ago. Today, the account balance is $1,500. If the account paid interest compounded annually, how much interest on interest was earned?
A.$86.20
B. $93.10
C. $102.39
D. $130.28
E. $500.00

Accessibility: Keyboard Navigation
Blooms: Apply
Difficulty: Medium
Learning Objective: 05-01 How to determine the future value of an investment made today.
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-03 Investing for More than One Period
Topic: 05-08 More on Present and Future Values
Topic: 05-09 Present versus Future Value
Topic: 05-10 Determining the Discount Rate

During years 2 and 3 combined, the account earned $10 compound interest. How much was in simple interest?
A.$30
B. $80
C. $105
D. $110
E. $120

Accessibility: Keyboard Navigation
Blooms: Apply
Difficulty: Medium
Learning Objective: 05-01 How to determine the future value of an investment made today.
Topic: 05-04 A Note on Compound Growth

What is the future value of $7,540 invested at 6.5% interest for seven years?
A.$10,330.45
B. $11,001.93
C. $11,041.26
D. $11,717.06
E. $11,337.37

You wish to have $200,000 at the end of twenty years. In the last five years, you withdraw $1,000 annually at a rate of 3.8% compounded quarterly. During the middle ten years, you contribute $500 monthly at a rate of 2.8% compounded semi-annually. Given this information, determine the initial deposit that has to be made at the start of the first five years at a rate of 4% compounded monthly.
A.$13,056.65
B. $12,056.65
C. $11,056.65
D. $10,056.65
E. $9,056.65

Accessibility: Keyboard Navigation
Blooms: Apply
Difficulty: Hard
Learning Objective: 05-02 How to determine the present value of cash to be received at a future date.
Topic: 05-07 Present Values for Multiple Periods

Wexter and Daughter invested $165,000 to help fund a company expansion project planned for 3 years from now. How much additional money will the firm have saved 3 years from now if it can earn 7% rather than 5% on this money?
A.$7,940.09
B. $8,218.07
C. $11,123.97
D. $12,648.18
E. $13,211.21

You have just landed your first job. Part of the offer includes a $4,000 new employee bonus which is intended to cover your relocation costs. You have determined that you can move yourself for $1,000. Thus, you have decided to open an Individual Retirement Account with the remaining $3,000. How much more will this investment be worth 35 years from now if you can earn an average rate of return of 9.5% rather than 9%?
A.$10,639.32
B. $10,676.16
C. $11,207.91
D. $11,341.41
E. $11,454.54

You have just been awarded a $200,000 insurance settlement. The insurance company has offered to invest this amount at a guaranteed interest rate of 4.5% for ten years. You think you can invest this money yourself and earn an average return of 8%. If you are able to do that, how much more will your settlement be worth ten years from now than if you had left the funds with the insurance company?
A.$78,829.69
B. $86,991.91
C. $118,009.42
D. $121,191.12
E. $137,188.23

Alpo, Inc. invested $500,000 to help fund a company expansion project scheduled for eight years from now. How much additional money will they have eight years from now if they can earn 9% rather than 7% on this money?
A.$58,829.69
B. $86,991.91
C. $118,009.42
D. $126,745.19
E. $137,188.23

Accessibility: Keyboard Navigation
Blooms: Apply
Difficulty: Medium
Learning Objective: 05-01 How to determine the future value of an investment made today.
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-01 Future Value and Compounding
Topic: 05-08 More on Present and Future Values
Topic: 05-09 Present versus Future Value

Your parents agree to pay half of the purchase price of a new car when you graduate from college. You will graduate and buy the car two years from now. You have $6,000 to invest today and can earn 10% on invested funds. If your parents match the amount of money you have in two years, what is the maximum you can spend on the new car?
A.$7,260
B. $11,948
C. $12,000
D. $13,250
E. $14,520

You wish to have $400,000 at the end of twenty-five years. In the last ten years, you contribute $1,000 semi-annually at a rate of 5.8% compounded monthly. During the middle ten years, you withdraw $750 quarterly at a rate of 4.5% compounded annually. Given this information, determine the initial deposit that has to be made at the start of the first five years at a rate of 4% compounded monthly.
A.$115,150.00
B. $120,150.00
C. $125,150.00
D. $130,150.00
E. $135,150.00

You will be receiving $5,000 from your family as a graduation present. You have decided to save this money for your retirement. You plan to retire thirty-five years after graduating. How much additional money will you have at that time if you can earn an average of 8.5% on your investment instead of just 8%?
A.$12,971.49
B. $13,008.47
C. $13,123.93
D. $13,234.44
E. $13,309.85

Accessibility: Keyboard Navigation
Blooms: Apply
Difficulty: Medium
Learning Objective: 05-01 How to determine the future value of an investment made today.
Topic: 05-01 Future Value and Compounding
Topic: 05-03 Investing for More than One Period

You just won the lottery and want to put some money away for your child’s college education. College will cost $65,000 in 18 years. You can earn 8% compounded annually. How much do you need to invest today?
A.$9,828.18
B. $11,763.07
C. $13,690.82
D. $15,258.17
E. $16,266.19

You would like to give your daughter $50,000 towards her college education 15 years from now. How much money must you set aside today for this purpose if you can earn 9% on your investments?
A.$12,250.00
B. $12,989.47
C. $13,726.90
D. $14,008.50
E. $14,211.11

You are scheduled to receive $18,000 in five years. When you receive it, you will invest it for five more years at 8.6% per year. How much will you have at the end of this time? What would be an equivalent Present Value?
A.$15,916
B. $14,916
C. $13,916
D. $12,916
E. $11,916

Accessibility: Keyboard Navigation
Blooms: Apply
Difficulty: Medium
Learning Objective: 05-02 How to determine the present value of cash to be received at a future date.
Topic: 05-05 Present Value and Discounting
Topic: 05-06 The Single-Period Case
Topic: 05-07 Present Values for Multiple Periods

A deposit of $10,000 increased to $12,500 in 5 years. Determine the annual rate of interest used and calculate the balance at the end of year four.
A.$11,954
B. $12,254
C. $13,954
D. $14,254
E. $15,954

Twenty years from now, you would like to purchase a cottage located on the shores of your favourite lake. You expect that you will have $250,000 available at that time for this purchase. You could afford a home that is currently selling for ____ if the homes increase in value by 3% annually, but if the homes increase in value by 5% annually, you can only afford a home priced at _____ today.
A.$127,023; $92,687
B. $138,419; $94,222
C. $138,419; $114,097
D. $144,676; $100,469
E. $144,676; $111,068

Accessibility: Keyboard Navigation
Blooms: Apply
Difficulty: Medium
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-08 More on Present and Future Values
Topic: 05-09 Present versus Future Value

What is the future value of $3,497 invested for 15 years at 7.5% compounded annually?
A.$7,431.13
B. $10,347.19
C. $14,289.16
D. $14,911.08
E. $15,267.21

Jessica invests $3,000 in an account that pays 5% simple interest. How much more could she have earned over a 7-year period if the interest had compounded annually?
A.$122.20
B. $129.20
C. $147.80
D. $171.30
E. $221.30

You would like to give your daughter $50,000 towards her college education sixteen years from now. How much money must you set aside today for this purpose if you can earn 7.8% on your funds?
A.$14,775.50
B. $15,033.84
C. $15,250.00
D. $16,245.33
E. $16,909.13

When you retire 36 years from now, you want to have $2 million. You think you can earn an average of 11.5% on your investments. To meet your goal, you are trying to decide whether to deposit a lump sum today, or to wait and deposit a lump sum 3 years from today. How much more will you have to deposit as a lump sum if you wait for 3 years before making the deposit?
A.$15,344.14
B. $15,677.78
C. $16,208.11
D. $17,021.12
E. $19,407.78

You want to have $260,000 saved 15 years from now. How much less do you have to deposit today to reach this goal if you can earn 8% rather than 7% on your savings?
A.$8,728.44
B. $12,273.13
C. $16,602.12
D. $17,414.41
E. $20,019.2

You would like to give your daughter $40,000 towards her college education thirteen years from now. How much money must you set aside today for this purpose if you can earn 6.3% on your funds?
A.$17,750.00
B. $17,989.28
C. $18,077.05
D. $18,213.69
E. $18,395.00

You would like to invest some money today such that your investment will be worth $100,000 fifteen years from now. Your broker gives you two options. First, you can invest at a guaranteed annual rate of 4%. Or, you can invest in stocks and hopefully earn an average of 7% per year. How much more will you have to invest today if you opt for the fixed rate rather than the stocks?
A.$18,145.45
B. $18,419.02
C. $18,623.18
D. $18,904.21
E. $19,281.85

When you retire forty years from now, you want to have $1 million. You think you can earn an average of 8.5% on your money. To meet this goal, you are trying to decide whether to deposit a lump sum today, or to wait and deposit a lump sum five years from today. How much more will you have to deposit as a lump sum if you wait for five years before making the deposit?
A.$18,001.06
B. $18,677.78
C. $18,998.03
D. $19,272.81
E. $21,036.83

Accessibility: Keyboard Navigation
Blooms: Apply
Difficulty: Medium
Learning Objective: 05-02 How to determine the present value of cash to be received at a future date.
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-05 Present Value and Discounting
Topic: 05-08 More on Present and Future Values
Topic: 05-09 Present versus Future Value

How much would you have to invest today at 8% compounded annually to have $25,000 available for the purchase of a car four years from now?
A.$18,267.26
B. $18,375.75
C. $19,147.25
D. $21,370.10
E. $22,149.57

What is the present value of $36,800 to be received 6 years from today if the discount rate is 12%?
A.$18,644.03
B. $19,407.18
C. $19,414.14
D. $20,211.08
E. $20,390.14

What is the present value of $2,800 to be received three years from now if the discount rate is 9.5%?
A.$2,114.48
B. $2,132.63
C. $2,361.48
D. $2,734.54
E. $3,676.21

Last year, you deposited $25,000 into a retirement savings account at a fixed rate of 7.5%. Today, you could earn a fixed rate of 8% on a similar type account. However, your rate is fixed and cannot be adjusted. How much less could you have deposited last year if you could have earned a fixed rate of 8% and still have the same amount as you currently will when you retire 40 years from today?
A.$1,218.46 less
B. $1,666.67 less
C. $2,408.28 less
D. $3,628.09 less
E. $4,331.30 less

Today Richard is investing $1,000 at 5% interest for five years. One year ago, Richard invested $1,000 at 6.25% for six years. How much money will Richard have saved in total five years from now if both investments compound interest annually?
A.$2,543.77
B. $2,641.98
C. $2,678.81
D. $2,630.36
E. $2,714.99

Your grandmother invested one lump sum 17 years ago at 4.25% interest. Today, she gave you the proceeds of that investment which totaled $5,539.92. How much did your grandmother originally invest?
A.$2,700.00
B. $2,730.30
C. $2,750.00
D. $2,768.40
E. $2,774.90

Andy promises Opie that he will give him $5,000 upon his graduation from college at Mayberry U. How much must Andy invest today to make good on his promise, if Opie is expected to graduate in 12 years and Andy can earn 5% on his money?
A.$2,135.32
B. $2,784.19
C. $2,881.11
D. $3,012.88
E. $8,979.28

Stephen invests $2,500 in an account that pays 6% simple interest. How much money will Stephen have at the end of three years?
A.$2,650
B. $2,809
C. $2,950
D. $2,978
E. $3,000

Alex and Courtney are each investing $1,200 today in a savings account. Alex will earn 4% interest compounded annually. Courtney will earn 4% simple interest. After five years Alex will have ____ more than Courtney.
A.$19.98
B. $20.13
C. $20.17
D. $20.21
E. $20.28

Accessibility: Keyboard Navigation
Blooms: Apply
Difficulty: Easy
Learning Objective: 05-01 How to determine the future value of an investment made today.
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-01 Future Value and Compounding
Topic: 05-08 More on Present and Future Values
Topic: 05-09 Present versus Future Value

You own a stamp collection that is currently valued at $24,500. If the value increases by 5.5% annually, how much will the collection be worth when you retire 40 years from now?
A.$204,113.07
B. $204,981.16
C. $205,155.45
D. $206,666.67
E. $208,576.07

Alexander Industries just had a very profitable year. The owner has decided to invest $225,000 of the profits in a venture that pays an 8% rate of return for fifteen years. How much more would the investment have been worth if the owner could have made 9% on this investment?
A.$52,910.25
B. $105,820.50
C. $211,641.00
D. $713,738.05
E. $819,558.55

You own a classic automobile that is currently valued at $67,900. If the value increases by 8% annually, how much will the automobile be worth 15 years from now?
A.$199,801.33
B. $212,524.67
C. $214,740.01
D. $215,390.28
E. $218,887.79

You have $500 in an account which pays 5% compound interest. How much additional interest would you earn over four years if you moved the money to an account earning 6%?
A.$21.89
B. $23.49
C. $24.93
D. $25.88
E. $29.94

You collect old model trains. One particular model increases in value at a rate of 6.5% per year. Today, the model is worth $1,670. How much additional money can you make if you wait 4 years to sell the model rather than selling it 2 years from now?
A.$196.67
B. $208.04
C. $241.79
D. $254.24
E. $280.15

You hope to buy your dream house six years from now. Today your dream house costs $189,900. You expect housing prices to rise by an average of 4.5% per year over the next six years. How much will your dream house cost by the time you are ready to buy it?
A.$240,284.08
B. $246,019.67
C. $246,396.67
D. $246,831.94
E. $247,299.20

Your goal is to have two separate investments that will be worth $10,000 each ten years from today. Investment A will pay 6% interest. Investment B will pay 6.5% interest. You will make a one-time deposit into each account today. What is the difference between the amount you must invest today in Investment A as compared to the amount you must invest today in Investment B if you are to reach your goal in ten years?
A.$241.92
B. $245.45
C. $256.69
D. $261.08
E. $263.47

What is the present value of $36,500 to be received five years from today if the discount rate is 6.75%?
A.$26,330.16
B. $26,678.19
C. $26,911.47
D. $28,008.19
E. $28,123.76

You are scheduled to receive $30,000 in three years. When you receive it, you will invest it for seven more years at 5.5% per year. How much will you have at the end of this time? What would be an equivalent Present Value?
A.$29,548
B. $28,548
C. $27,548
D. $26,548
E. $25,548

An investor is considering depositing $20,000 in an account earning 5% compounded quarterly for the next three years. Afterwards, he will take this amount and contribute $200 quarterly for the next four years at a rate of 4% compounded semi-annually. Finally, over the next two years, he will withdraw $1,000 annually at a rate of 3.5% compounded monthly. Determine the future value at the end of this time period.
A.$33,833.94
B. $30,833.94
C. $27,833.94
D. $24,833.94
E. $21,833.94

Accessibility: Keyboard Navigation
Blooms: Apply
Difficulty: Hard
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-08 More on Present and Future Values
Topic: 05-09 Present versus Future Value

Your goal is to build your first home seven years from now. The home that you desire currently costs $215,900. New home prices are increasing by 4.2% annually. If home prices continue rising at that pace, how much will your home cost when you are ready to build seven years from now?
A.$281,113.21
B. $284,109.67
C. $287,956.36
D. $292,001.06
E. $295,474.06

You hope to buy your dream house 3 years from now. Today, your dream house costs $247,900. You expect housing prices to rise by an average of 7.5% per year over the next 3 years. How much will your dream house cost by the time you are ready to buy it?
A.$292,063.48
B. $294,882.01
C. $298,600.00
D. $307,965.40
E. $309,425.45

Frank invests $2,500 in an account that pays 6% simple interest. How much money will he have at the end of four years?
A.$2,650
B. $3,100
C. $3,156
D. $3,163
E. $10,600

Your goal is to have $50,000 in cash to build a new home twelve years from now. Your plan is to make one deposit today to fund this goal. How much more will you have to deposit today to fund this goal if you can only earn 4% on your savings rather than 5%?
A.$3,104.11
B. $3,188.87
C. $3,218.07
D. $3,273.16
E. $3,387.98

Jeff invests $3,000 in an account that pays 7% simple interest. How much more could he have earned over a 20-year period if the interest had compounded annually?
A.$2,840.00
B. $3,212.12
C. $3,778.54
D. $4,087.18
E. $4,409.05

When you retire thirty years from now, you want to have $750,000. You think you can earn an average of 9% on your money. To meet this goal, you are trying to decide whether to deposit a lump sum today, or to wait and deposit a lump sum five years from today. How much more will you have to deposit as a lump sum if you wait for five years before making the deposit?
A.$28,788.03
B. $29,414.14
C. $30,447.52
D. $36,118.09
E. $38,278.27

Jeanette needs $15,000 as a down payment for a house six years from now. She earns 3.5% on her savings. Jeanette can either deposit one lump sum today for this purpose or she can wait a year and deposit a lump sum. How much additional money must Jeanette deposit if she waits for one year rather than making the deposit today?
A.$121.03
B. $166.67
C. $307.00
D. $333.33
E. $427.09

You will receive a $100,000 inheritance in 20 years. You can invest that money today at 6% compounded annually. What is the present value of your inheritance?
A.$27,491.53
B. $29,767.15
C. $31,180.47
D. $35,492.34
E. $100,000.00

Jennifer invested $2,000 in an account that pays 3% simple interest. How much more could she have earned over a six-year period if the interest had compounded annually?
A.$28.10
B. $29.18
C. $31.50
D. $33.33
E. $34.67

What is the future value of $25,000 received today if it is invested at 6.5% compounded annually for six years?
A.$17,133.35
B. $27,476.42
C. $36,478.56
D. $39,521.75
E. $41,374.89

You collect model airplanes. One particular model is currently valued at $275. If this model increases in value by 5% annually, it will be worth ____ six years from now and _____ twelve years from now.
A.$368.01; $442.89
B. $368.01; $461.34
C. $368.53; $442.89
D. $368.53; $467.08
E. $368.53; $493.86

Your older sister deposited $5,000 today at 8% interest for five years. You would like to have just as much money at the end of the next five years as your sister. However, you can only earn 6% interest. How much more money must you deposit today than your sister if you are to have the same amount at the end of five years?
A.$201.80
B. $367.32
C. $399.05
D. $423.81
E. $489.84

Robin invested $10,000 in an account that pays 5% simple interest. How much more could she have earned over a 40-year period if the interest had compounded annually?
A.$38,207.16
B. $38,414.14
C. $40,399.89
D. $48,414.14
E. $50,399.89

An account paying annual compound interest was opened with $1,000 ten years ago. Today, the account balance is $1,500. If the same interest rate is offered on an account paying simple interest, how much income would be earned each year over the same time period?
A.$36.97
B. $40.41
C. $40.75
D. $41.38
E. $50.00

An account paying annual compound interest was opened with $1,000 ten years ago. Today, the account balance is $1,500. If the same interest rate is offered on an account paying simple interest, how much income would be earned over the same time period?
A.$86.20
B. $92.47
C. $413.80
D. $436.29
E. $500.00

Today you earn a salary of $28,500. What will be your annual salary fifteen years from now if you earn annual raises of 3.5%?
A.$47,035.35
B. $47,522.89
C. $47,747.44
D. $48,091.91
E. $48,201.60

Theresa wants to save $10,000 so that she can surprise her husband with a vacation six years from now. She can earn 7% on her savings. How much more will she have to deposit if she waits one more year before investing versus if she deposits one lump sum today?
A.$466.44
B. $469.15
C. $470.23
D. $471.08
E. $471.54

Faith invests $4,500 in an account that pays 4% simple interest. How much money will she have at the end of eight years?
A.$4,680
B. $5,367
C. $5,940
D. $6,122
E. $6,159

You will be receiving $2,500 from your family as a graduation present. You have decided to save this money for your retirement. You plan to retire 40 years after graduation. How much additional money will you have at that time if you can earn an average of 12.5% on your investment instead of just 12%?
A.$45,370.08
B. $51,400.62
C. $53,018.97
D. $58,811.99
E. $64,367.48

Lisa deposited $500 in a savings account this morning. The account pays 2.5% simple interest. If Lisa leaves this money in the account for five years, how much total interest will she earn?
A.$10.75
B. $12.50
C. $53.75
D. $62.50
E. $67.25

Many economists view a 3% annual inflation rate as “acceptable”. Assuming a 3% annual increase in the price of automobiles, how much will a new Suburban cost you five years from now, if today’s price is $48,000?
A.$41,405
B. $48,000
C. $54,024
D. $55,200
E. $55,645

Today, you earn a salary of $37,800. What will your annual salary be twelve years from now if you receive annual raises of 3.6%?
A.$55,981.03
B. $56,324.17
C. $56,907.08
D. $57,784.17
E. $58,213.46

Your big brother deposited $10,000 today at 9% interest for 6 years. You would like to have just as much money at the end of the next 6 years as your brother. However, you can only earn 7.5% interest. How much more money must you deposit today than your brother did if you are to have the same amount at the end of the 6 years?
A.$398.68
B. $487.63
C. $575.00
D. $648.21
E. $866.96

Today, you earn a salary of $42,500. What will be your annual salary 10 years from now if you earn annual raises of 3.2%?
A.$56,100.00
B. $57,414.06
C. $58,235.24
D. $59,122.08
E. $59,360.45

You setup an educational savings plan that will pay $15,000 to your newborn child in 18 years. If the plan uses a rate of 4.75% per year, what was contributed into this plan?
A.$4,459
B. $5,800
C. $6,506
D. $7,007
E. $8,576

Cooper invests $6,500 in a savings account at his local bank. The bank pays 2.75% simple interest. Cooper does not make any additional withdrawals or deposits to this account. How much will his account be worth after 12 years?
A.$2,145
B. $2,655
C. $6,679
D. $8,645
E. $9,001

You received a $1 savings account earning 5% on your 1^stbirthday. How much will you have in the account on your 40^thbirthday if you don’t withdraw any money before then?
A.$5.89
B. $6.34
C. $6.70
D. $7.00
E. $7.04

Which of the following will result in a future value greater than $100?
A.$40 deposited now with an annual interest rate of 14% for 8 years.
B. $60 deposited now with an annual interest rate of 12% for 4 years.
C. $60 deposited now with an annual interest rate of 8% for 6 years.
D. $80 deposited now with an annual interest rate of 7% for 3 year.
E. $80 deposited now with an annual interest rate of 10% for 2 year.

Accessibility: Keyboard Navigation
Blooms: Understand
Difficulty: Medium
Learning Objective: 05-01 How to determine the future value of an investment made today.
Topic: 05-01 Future Value and Compounding
Topic: 05-02 Investing for a Single Period
Topic: 05-03 Investing for More than One Period

You want to have $10,000 saved ten years from now. How much less do you have to deposit today to reach this goal if you can earn 6% rather than 5% on your savings?
A.$555.18
B. $609.81
C. $615.48
D. $928.73
E. $1,046.22

You deposit $500,000 in a higher risk investment. Three years later, you receive $711,900 and withdraw your funds. Given this information calculate the balance at the end of year two.
A.$665,202
B. $632,804
C. $636,549
D. $687,702
E. $693,303

Betty invests $500 in an account that pays 3% simple interest. How much money will Betty have at the end of ten years?
A.$630.00
B. $633.33
C. $650.00
D. $671.96
E. $675.00

Antoinette needs $20,000 as a down payment for a house five years from now. She earns 4% on her savings. Antoinette can either deposit one lump sum today for this purpose or she can wait a year and deposit a lump sum. How much additional money must Antoinette deposit if she waits for one year rather than making the deposit today?
A.$639.19
B. $657.54
C. $658.23
D. $659.04
E. $800.00

You own a classic automobile that is currently valued at $39,500. If the value increases by 6% annually, how much will the auto be worth ten years from now?
A.$64,341.34
B. $44,734.42
C. $69,843.06
D. $70,738.48
E. $74,146.93

Your grandmother invested one lump sum 42 years ago at 3.5% interest. Today, she gave you the proceeds of that investment which totaled $28,204.37. How much did your grandmother originally invest?
A.$4,500
B. $6,650
C. $7,200
D. $7,500
E. $9,000

You deposit $1,000 in a retirement account today at 8.5% interest. How much more money will you have if you leave the money invested for 40 years rather than 35 years?
A.$7,714.91
B. $7,799.08
C. $7,839.73
D. $7,846.52
E. $8753.37

The James Co. plans on saving money to buy some new equipment. The company is opening an account today with a deposit of $15,000 and expects to earn 4% interest. After 3 years, the firm wants to add an additional $50,000 to the account. If the account continues to earn 4%, how much money will the James Co. have in their account five years from now?
A.$66,872.96
B. $68,249.79
C. $70,952.96
D. $72,329.79
E. $81,361.18

Accessibility: Keyboard Navigation
Blooms: Apply
Difficulty: Hard
Learning Objective: 05-01 How to determine the future value of an investment made today.
Topic: 05-01 Future Value and Compounding
Topic: 05-02 Investing for a Single Period
Topic: 05-03 Investing for More than One Period

The Smith Co. has $450,000 to invest at 5.5% interest. How much more money will they have if they invest these funds for eight years instead of five years?
A.$62,948.21
B. $68,851.36
C. $74,250.00
D. $78,408.62
E. $102,476.93

You deposit $3,000 in a retirement account today at 5.5% interest. How much more money will you have if you leave the money invested for forty-five years rather than forty years?
A.$7,714.91
B. $7,799.08
C. $7839.74
D. $7,846.52
E. $7,858.19

You deposit $500,000 in a higher risk investment. Three years later, you receive $711,900 and withdraw your funds. Given this information calculate the interest earned at the end of year 3.
A.$77,096
B. $78,806
C. $79,096
D. $80,806
E. $81,096

What is the future value of $4,160 invested for eight years at 8.5% compounded annually?
A.$6,988.80
B. $7,989.71
C. $8,122.20
D. $8,211.29
E. $8,404.12

Martha is going to receive $6,000 in two years from Tom. She will receive an additional $4,000 in three years from Tom. She earns 7.15% on her investments. How much is this money from Tom worth to Martha today?
A.$7,893.46
B. $8,477.47
C. $8,891.74
D. $9,225.97
E. $9,251.50

The Blackwell Co. expects to receive $135,000 from an insurance settlement four years from now. If the company can earn 11% on its investments, what is the value of the insurance settlement worth today?
A.$85,368.94
B. $87,693.43
C. $88,928.68
D. $130,161.39
E. $140,018.48

Today, your grandmother gave you a gift of $25,000 to help pay for your college education. She told you that this amount was the result of a one-time investment at 8% interest 13 years ago. How much did your grandmother originally invest?
A.$9,192.45
B. $9,225.00
C. $9,350.00
D. $9,419.25
E. $9,504.55

Omar has an investment valued at $12,345 today. He made a one-time investment at 6.5% four years ago. Leon has an investment that is also valued at $12,345 today. Leon invested four years ago at 7.5%. Omar originally invested _____ and Leon invested _____.
A.$9,568.24; $9,199.16
B. $9,596.05; $9,243.94
C. $9,608.14; $9,267.67
D. $9,633.33; $9,304.06
E. $9,652.18; $9,389.00

The future value interest factor is calculated as:
A.(1 + r)^t
B. (1 + rt)
C. (1 + r)(t)
D. 1 + r – t
E. (1 + r)(2)

Accessibility: Keyboard Navigation
Blooms: Remember
Difficulty: Easy
Learning Objective: 05-01 How to determine the future value of an investment made today.
Topic: 05-01 Future Value and Compounding
Topic: 05-02 Investing for a Single Period
Topic: 05-03 Investing for More than One Period

Lakeside Inc. invested $735,000 at an 11.25% rate of return. The company sold their investment for $1,067,425. How much longer would Lakeside have had to wait if they had wanted to sell their investment for $1.25 million?
A..98 year
B. 1.48 years
C. 1.98 years
D. 2.31 years
E. 3.50 years

The present value interest factor is calculated as:
A.1/(1 + r – t)
B. 1/(1 + rt)
C. 1/(1 + r)(t)
D. 1/(1 + r)^t
E. 1 + r + t

Gretchen Enterprises borrowed $149,500 for two years from the bank. At the end of the two years, they repaid the loan with one payment of $176,590. What was the interest rate on the loan?
A.8.68%
B. 9.06%
C. 10.00%
D. 10.42%
E. 18.12%

Thirty years ago, your father invested $6,000. Today that investment is worth $67,270.98. What is the average rate of return your father earned on this investment?
A.8.39%
B. 8.44%
C. 10.23%
D. 10.34%
E. 11.67%

One year ago, you invested $2,500. Today it is worth $2,789.50. What rate of interest did you earn?
A.8.67%
B. 9.89%
C. 10.67%
D. 11.42%
E. 11.58%

Tropical Tans is saving money to build a new salon. Three years ago, they set aside $12,000 for this purpose. Today, that account is worth $16,418. What rate of interest is Tropical Tans earning on this money?
A.10.88%
B. 10.97%
C. 11.01%
D. 11.14%
E. 11.23%

Thirty years ago, your father invested $11,000. Today, that investment is worth $287,047.
What is the average annual rate of return your father earned on his investment?
A.11.14%
B. 11.27%
C. 11.38%
D. 11.49%
E. 12.07%

In 1889, Vincent Van Gogh’s painting, “Sunflowers,” sold for $125. One hundred years later it sold for $36 million. Had the painting been purchased by your great-grandfather and passed on to you, what annual return on investment would your family have earned on the painting?
A.9.11%
B. 10.09%
C. 11.88%
D. 11.99%
E. 13.40%

At a 6% rate of interest you will double your money in approximately ___ years.
A.3
B. 6
C. 12
D. 24
E. 48

Accessibility: Keyboard Navigation
Blooms: Understand
Difficulty: Easy
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-11 Finding the Number of Periods

At a 3% rate of interest, you will quadruple your money in approximately ____ years.
A.3
B. 6
C. 12
D. 24
E. 47

You need $2,000 to buy a new stereo for your car. If you have $800 to invest at 5% compounded annually, how long will you have to wait to buy the stereo?
A.6.58 years
B. 8.42 years
C. 14.58 years
D. 15.75 years
E. 18.78 years

An investor deposited $10,500 in an account. At the end of year four, the account had accumulated $5,728.88. Over the first four years, the account earned ________ compounded annually.
A.11.5%
B. 12.8%
C. 14.6%
D. 15.6%
E. 23.1%

Koji invested $3,300 at 7.75% interest. After a period of time he withdrew $9,383.31. How long did Koji have his money invested?
A.13 years
B. 14 years
C. 15 years
D. 16 years
E. 17 years

Six years ago, Marti invested $3,500 in an account. No other investments or withdrawals have been made. Today the account is worth $7,403.16. What rate of return has Marti earned thus far?
A.12.86%
B. 13.30%
C. 15.96%
D. 18.58%
E. 19.20%

Sue invested $5,000 eleven years ago at 12%. Terri has the same amount saved today as Sue has. Terri also earns 12% but she only invested $2,500. How long ago did Terri invest her money?
A.17.1 years
B. 17.4 years
C. 17.9 years
D. 21.5 years
E. 22.0 years

Granny puts $35,000 into a bank account earning 4%. You can’t withdraw the money until the balance has doubled. How long will you have to leave the money in the account?
A.16 years
B. 17 years
C. 18 years
D. 19 years
E. 20 years

An account was opened with an investment of $1,000 ten years ago. The ending balance in the account is $1,500. If interest was compounded annually, what rate was earned on the account?
A.1.0%
B. 2.2%
C. 2.9%
D. 3.8%
E. 4.1%

Chia Burgers began operations by opening 115 restaurants in Western Canada at the end of its first year of operations. By the end of year 2, an additional 5 restaurants were opened. By the end of year 3, there were 130 restaurants operational. At the end of year 5, there were 138 total restaurants.
If, over the next five years, eating establishments are expected to grow at the annual growth rate as they did during years 1 to 5, forecast the number of eating establishments at the end of year 10.
A.172
B. 198
C. 202
D. 223
E. 225

One year ago, you invested $5,000. Today, your investment is worth $6,178.40. What rate of interest did you earn?
A.16.23%
B. 16.45%
C. 22.18%
D. 23.57%
E. 24.09%

The price of gold has gone from $250 an ounce to approximately $1,600. Given an annual growth rate of 8.04%, how long did it take gold to reach its highest value?
A.27 years
B. 26 years
C. 25 years
D. 24 years
E. 23 years

Moe and Joe are twins. Moe invested $1,000, earned 9% annually, and now has $1,992.56. Joe invested $1,000, earned 6.47%, and now has $1,992.97. Joe invested his money _____ years before Moe.
A.2.5 years
B. 2.8 years
C. 3.0 years
D. 3.2 years
E. 3.5 years

Alpha, Inc. is saving money to build a new factory. Six years ago they set aside $250,000 for this purpose. Today, that account is worth $306,958. What rate of interest is Alpha earning on this money?
A.3.43%
B. 3.45%
C. 3.48%
D. 3.52%
E. 3.55%

Sampson, Inc. invested $1.325 million in a project that earned an 8.25% rate of return. Sampson sold their investment for $3,713,459. How much sooner could Sampson have sold the company if they only wanted $3 million from the project?
A.2.69 years
B. 3.33 years
C. 5.17 years
D. 6.67 years
E. 10.31 years

Chia Burgers began operations by opening 115 restaurants in Western Canada at the end of its first year of operations. By the end of year 2, an additional 5 restaurants were opened. By the end of year 3, there were 130 restaurants operational. At the end of year 5, there were 138 total restaurants.
From the end of year 1 to the end of year 5, the number of eating establishments grew at a rate of ____________ compounded annually.
A.4.2%
B. 4.7%
C. 5.6%
D. 8.7%
E. 9.3%

Chia Burgers began operations by opening 115 restaurants in Western Canada at the end of its first year of operations. By the end of year 2, an additional 5 restaurants were opened. By the end of year 3, there were 130 restaurants operational. At the end of year 5, there were 138 total restaurants.
Between the end of year 2 and the end of year 3, the number of eating establishments grew at a rate of _________ compounded annually.
A.4.2%
B. 4.7%
C. 5.6%
D. 8.3%
E. 9.3%

If the town’s population was 62,000 at the end of year 5, and the population grew at the same annual rate as the number of eating establishments between the end of year 1 and the end of year 5, what was the town’s population at the end of year 1 if the annual growth rate is 5.626%?
A.49,809
B. 51,435
C. 53,230
D. 54,330
E. 56,730

Which one of the following interest rates will produce the largest value at the end of ten years given a lump sum investment of $5,000?
A.5.5%, compounded annually
B. 5.5%, simple interest
C. 6.0%, simple interest
D. 6.0%, compounded annually
E. 6.0%, compounded semi-annually

All County Insurance, Inc. promises to pay Ted $1 million on his 65^thbirthday in return for a one-time payment of $75,000 today. (Ted just turned 25) At what rate of interest would Ted be indifferent between accepting the company’s offer and investing the premium on his own?
A.2.4%
B. 5.5%
C. 6.1%
D. 6.7%
E. 7.2%

Five years ago, Precision Tool set aside $50,000 in case of a financial emergency. Today, that account has increased in value to $64,397. What rate of interest is the firm earning on this money?
A.5.19%
B. 5.47%
C. 6.18%
D. 6.32%
E. 6.45%

Thirty years ago, an average house cost $120,000 in Vancouver. Now the average house price is $950,000. Determine the annual rate of growth in Vancouver’s housing prices.
A.8.31%
B. 7.14%
C. 6.25%
D. 5.58%
E. 4.63%

New Metals, Inc. is planning on expanding their operations when the economy strengthens in a few years. At that time they will need to purchase additional equipment. Four years ago, they set aside $300,000 in a special account for this purpose. Today, that account is worth $383,048.98. What rate of interest is New Metals earning on this money?
A.5.87%
B. 5.92%
C. 6.26%
D. 6.30%
E. 6.35%

Kay purchased some land costing $124,600. Today, that same land is valued at $179,400. How long has she owned this land if the price of land has been increasing at 6% per year?
A.5.95 years
B. 6.26 years
C. 6.33 years
D. 6.50 years
E. 6.57 years

Chia Burgers began operations by opening 115 restaurants in Western Canada at the end of its first year of operations. By the end of year 2, an additional 5 restaurants were opened. By the end of year 3, there were 130 restaurants operational. At the end of year 5, there were 138 total restaurants.
If the number of eating establishments is expected to grow in year 6 at the same rate as the percentage increase in year 5, how many new eating establishments will be added in year 6?
A.5
B. 6
C. 7
D. 8
E. 9

Stephen has $2,400 to invest. Which one of the following investment options will produce the largest future value for him?
A.7% simple interest for 10 years
B. 7%, compounded annually for 10 years
C. 7%, compounded monthly for 12 years
D. 7%, compounded annually for 12 years
E. 7, simple interest for 12 years

Six years ago, Home Health Industries (HHI) adopted a plan to expand its services next year. At the time the plan was adopted, HHI set aside $125,000 in excess funds to be held for this purpose. As of today, that money has increased in value to $186,408. What rate of interest is the firm earning on these funds?
A.6.89%
B. 7.10%
C. 7.18%
D. 7.27%
E. 7.43%

Some time ago, Richard purchased five acres of land costing $123,400. Today, that land is valued at $189,700. How long has he owned this land if the price of land has been increasing at 5.5% per year?
A.6.01 years
B. 6.98 years
C. 7.42 years
D. 8.03 years
E. 8.67 years

Approximately 13,500 students enrolled at Kwantlen University five years ago. Today, enrolment reached 18,800 students. Determine the annual growth rate in student enrolment.
A.5.55%
B. 6.85%
C. 7.65%
D. 8.25%
E. 9.55%

Forty years ago, your father invested $2,500. Today that investment is worth $107,921. What is the average rate of return your father earned on his investment?
A.8.50%
B. 9.33%
C. 9.50%
D. 9.87%
E. 9.99%

The price of fuel has tripled over the past fifteen years. Determine the rate of growth over this time period.
A.7.6%
B. 8.7%
C. 9.6%
D. 10.5%
E. 11.3%

Your grandfather placed $2,000 in a trust fund for you. In 10 years the fund will be worth $5,000. What is the rate of return on the trust fund?
A.5.98%
B. 8.76%
C. 9.60%
D. 9.98%
E. 10.14%

The process of finding the present value of some future amount is often called:
A.Growth.
B. Discounting.
C. Accumulation.
D. Compounding.
E. Reduction.

On your thirteenth birthday, you received $1,000 which you invested at 6.5% interest, compounded annually. Your investment is now worth $5,476. How old are you today?
A.age 29
B. age 32
C. age 35
D. age 37
E. age 40

When you were 26 years old, you received an inheritance of $1,500 from your grandfather. You invested that amount in Nu-Wave stock and have not touched the investment since then. Today, this investment is worth $109,533.59. Nu-Wave stock has earned an average rate of return of 11.3% per year over this time period. How old are you today?
A.age 57
B. age 59
C. age 62
D. age 64
E. age 66

On your tenth birthday, you received $100 which you invested at 4.5% interest, compounded annually. That investment is now worth $3,000. How old are you today?
A.age 77
B. age 82
C. age 84
D. age 86
E. age 87

The process of accumulating interest on an investment over time to earn more interest is called:
A.Growth.
B. Compounding.
C. Aggregation.
D. Accumulation.
E. Discounting.

Accessibility: Keyboard Navigation
Blooms: Remember
Difficulty: Easy
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-08 More on Present and Future Values
Topic: 05-10 Determining the Discount Rate

Five friends all open investment accounts today. Which one will withdraw the largest amount of money from their account assuming that they each withdraw their funds at the end of their initial investment period?
A.John, who invests $1,000 for eight years at 6% simple interest.
B. Terry, who invests $1,000 for four years at 9% with interest compounded annually.
C. Alicia, who invests $800 for ten years at 11% with interest compounded annually.
D. Kristi, who invests $1,200 for six years at 8% simple interest.
E. Roger, who invests $900 for nine years at 9% with interest compounded annually.

Neal wants to borrow $2,500 and has received the offers from his local banks. Which offer should Neal accept if he wants to repay the loan in one single payment two years from now?
A.Bank A, which offers a simple rate of 4%.
B. Bank B, which offers a simple rate of 5%.
C. Bank C, which offers a rate of 4% compounded annually.
D. Bank D, which offers a rate of 5% compounded annually.
E. Bank E, which offers a rate of 5% compounded monthly.

Isabelle wants to invest $1,000. She wants to withdraw her money three years from now. Which bank should she use if she wishes to maximize her investment?
A.Bank A, which offers a simple rate of 4%.
B. Bank B, which offers a simple rate of 5%.
C. Bank C, which offers a rate of 4% compounded annually.
D. Bank D, which offers a rate of 5% compounded monthly.
E. Bank E, which offers a rate of 5% compounded annually.

An account was opened with $1,000 three years ago. Today, the account balance is $1,157.63. If the account earns simple interest, how long will it take until the account has earned a total of $225 in interest?
A.Less than one more year.
B. Between one and two more years.
C. Between two and three more years.
D. Between three and four more years.
E. Between four and five more years.

Accessibility: Keyboard Navigation
Blooms: Understand
Difficulty: Medium
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-08 More on Present and Future Values
Topic: 05-09 Present versus Future Value
Topic: 05-10 Determining the Discount Rate
Topic: 05-11 Finding the Number of Periods

Monika has $6,000 in her investment account. She wants to withdraw her funds when her account reaches $10,000. A decrease in the rate of return she earns will:
A.Increase the value of her account faster.
B. Cause her to wait longer before withdrawing her money.
C. Cause the present value of her account to decrease.
D. Allow her to withdraw more money sooner.
E. Cause the compounding effect to increase.

You are choosing between investments offered by two different banks. One promises a return of 10% for three years using simple interest while the other offers a return of 10% for three years using compound interest. You should:
A.Choose the simple interest option because both have the same basic interest rate.
B. Choose the compound interest option because it provides a higher return.
C. Choose the compound interest option only if the compounding is for monthly periods.
D. Choose the simple interest option only if compounding occurs more than once a year.
E. Choose the compound interest option only if you are investing less than $5,000.

Accessibility: Keyboard Navigation
Blooms: Understand
Difficulty: Easy
Learning Objective: 05-01 How to determine the future value of an investment made today.
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-03 Investing for More than One Period
Topic: 05-08 More on Present and Future Values

The interest rate used to calculate the present value of future cash flows is called the ____________ rate.
A.Free interest.
B. Annual interest.
C. Compound interest.
D. Simple interest.
E. Discount.

The rate used to find the present value of a future payment is called the:
A.Simple rate.
B. Discount rate.
C. Compound rate.
D. Future value rate.
E. Loan rate.

The concept that a dollar received today is worth more than a dollar received tomorrow is referred to as the:
A.Present value.
B. Simple interest value.
C. Compound value.
D. Time value of money.
E. Future value of money.

The interest rate used to calculate the present value of future cash flows is called the _____ rate.
A.Free.
B. Annual.
C. Compound.
D. Simple.
E. Discount.

The rate of return used when computing a present value is referred to as the ______ rate while the rate used when computing a future value is referred to as the _____ rate.
A.Compound; discount.
B. Compound; simple.
C. Compound; compound.
D. Discount; discount.
E. Discount; compound.

As long as the interest rate is greater than zero, the present value of a single sum will always:
A.Increase as the interest rate increases.
B. Be less than the future value.
C. Decrease as the period of time decreases.
D. Equal the future value if the time period is one year.
E. Increase as the number of periods increases.

To create the same future value given a stated discount rate, you can:
A.Decrease both the present value and the time period.
B. Increase both the present value and the time period.
C. Decrease the time period and hold the present value constant.
D. Increase the present value and hold the time period constant.
E. Increase the present value and decrease the time period.

As the discount rate increases, the present value of $500 to be received six years from now:
A.Remains constant.
B. Also increases.
C. Decreases.
D. Becomes negative.
E. Will vary but the direction of the change is unknown.

The term to convert a future value amount into its present value is:
A.Annuitize
B. Compound
C. Discount
D. Multiply
E. Amortize

Accessibility: Keyboard Navigation
Blooms: Remember
Difficulty: Medium
Learning Objective: 05-01 How to determine the future value of an investment made today.
Topic: 05-01 Future Value and Compounding
Topic: 05-02 Investing for a Single Period
Topic: 05-03 Investing for More than One Period

To decrease the amount required today to fund a $10,000 debt due two years from now, you could _____ on your savings.
A.Increase the rate of interest earned
B. Decrease the number of compounding periods per year
C. Earn simple interest rather than compound interest
D. Both decrease the rate of interest and the number of compounding periods per year
E. Either decrease the rate of interest or decrease the number of compounding periods per year

The term interest-on-interest refers to:
A.The payment of interest more than once per year.
B. The interest earned on previous interest earnings which were reinvested.
C. Earning interest on an investment for a period greater than one year.
D. Earning interest only on the principal amount invested.
E. The process of accumulating interest on an investment over time to earn more interest.

Calculating the present value of a future cash flow to determine its value today is called:
A.Discounted cash flow valuation.
B. The discount rate.
C. Future value compounding.
D. Present value compounding.
E. Timing the cash flow.

On a financial calculator, the symbol “N” represents the:
A.Current value.
B. Time periods.
C. Future value.
D. Rate of simple interest.
E. Rate of compound interest.

Accessibility: Keyboard Navigation
Blooms: Remember
Difficulty: Easy
Learning Objective: 05-01 How to determine the future value of an investment made today.
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-03 Investing for More than One Period
Topic: 05-11 Finding the Number of Periods

The discounted value of money is called the:
A.Compound value.
B. Simple value.
C. Future value.
D. Complex value.
E. Present value.

Mary plans on saving $1,000 a year for ten years. She would like to know the value of these savings today. Mary should solve for the:
A.Present value.
B. Present value factor.
C. Future value.
D. Future value factor.
E. Compounded value.

The future value of C invested at r% for t periods is:
A.FV = C/(1 + r)^t.
B. FV = (C)(1 + t)^r.
C. FV = (C)(1 + r)^t.
D. FV = [C][1/(1 + r)^t].
E. FV = (C)(1 + r)(t).

Sun Lee has $500 today. Which one of the following statements is correct if she invests this money at a positive rate of interest for five years?
A.The higher the interest rate she earns, the less money she will have in the future.
B. The higher the interest rate, the longer she has to wait for her money to grow to $1,000 in value.
C. If Sun Lee can earn 7%, she will have to wait about six years to have $1,000 total.
D. At the end of the five years Sun Lee will have less money if she invests at 5% rather than at 7%.
E. At 10% interest Sun Lee should expect to have $1,000 in her account at the end of the five years.

Katie is going to receive $1,000 three years from now. Wilt is going to receive $1,000 five years from now. Which one of the following statements is correct if both Katie and Wilt apply a 5% discount rate to these amounts?
A.The present value of Katie and Wilt’s money is equal.
B. The value of Wilt’s money will be greater than the value of Katie’s money six years from now.
C. In today’s dollars, Wilt’s money is worth more than Katie’s.
D. In five years, the value of Katie’s money will be less than the value of Wilt’s money.
E. Katie’s money is worth more than Wilt’s money today.

You invest $1,000 in an account paying 5% simple interest. You do not add nor withdraw any funds from this account. Every year, your account balance will:
A.Remain constant.
B. Increase at an increasing rate.
C. Increase at a constant rate.
D. Increase at a decreasing rate.
E. Increase by a constant amount.

Compound interest means that you earn:
A.Interest only on the initial amount invested.
B. Interest on the initial principal only.
C. Interest on both the principal and prior reinvested interest.
D. A decreasing amount of interest each year.
E. The same amount of interest each year.

Isaac and Faith both want to have $5,000 in three years. Isaac expects to earn 8% on his investments and Faith expects a 7% rate of return. Which one of the following statements is correct concerning the amount of money they each need to invest today?
A.Faith needs to deposit $112.33 more than Isaac today.
B. Faith needs to deposit $173.33 more than Isaac today.
C. Isaac needs to deposit $3,699.16 today.
D. Faith needs to deposit $3,081.49 today.
E. Both Faith and Isaac should deposit $3,969.16 today.

Ito invested $4,350. After seven years he had an account value of $6,980.58. Maria invested $5,920. After six years she had an account value of $8,834.62. Which one of the following statements is correct?
A.Maria earned a rate of interest that was 0.9% higher than Ito’s rate.
B. Maria earned a rate of interest of 5.89%.
C. Ito earned a rate of interest that was 0.09% higher than Maria’s rate.
D. Ito earned a rate of interest of 6.90%.
E. Both Ito and Maria earned the same rate of interest.

Twelve years ago, Jake invested $2,000. Six years ago, Tami invested $4,000. Today, both Jake’s and Tami’s investments are each worth $9,700. Assume that both Jake and Tami continue to earn their respective rates of return. Which one of the following statements is correct concerning these investments?
A.Three years from today, Jake’s investment will be worth more than Tami’s.
B. One year ago, Tami’s investment was worth more than Jake’s.
C. Jake has earned a higher rate of return than Tami.
D. Tami has earned an average annual interest rate of 15.91%.
E. Jake has earned an average annual interest rate of 15.47%.

Ten years ago, Joe invested $5,000. Five years ago, Marie invested $2,500. Today, both Joe and Marie’s investments are each worth $8,500. Which one of the following statements is correct concerning their investments?
A.Three years from today, Joe’s investment will be worth more than Marie’s.
B. Last year, Marie’s investment was worth more than Joe’s.
C. Joe has earned more interest on interest than Marie.
D. Marie earned an annual interest rate of 27.73%.
E. Joe earned an annual interest rate of 6.45%.

Kurt invests $1,000 at a 10% rate of return for twenty years. The return is based on simple interest that is paid at the end of each year. Which one of the following is correct?
A.Kurt will receive more interest in year twenty than in year one.
B. Kurt will receive the same amount of interest each year.
C. Kurt will not receive any interest for the first year.
D. Kurt will receive less interest in year twelve than in year eight.
E. Kurt will receive interest on both the principal and year one’s interest in year two.

The greater the number of years, the:
A.Smaller the future value of a single sum.
B. Larger the present value of a single sum.
C. Larger the present value factor.
D. Smaller the future value factor.
E. Greater the compounding effect.

Accessibility: Keyboard Navigation
Blooms: Remember
Difficulty: Medium
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-11 Finding the Number of Periods

Twenty years ago, Max invested $10,000. Thirty years ago, Julie invested $5,000. Today, both Max and Julie’s investments are each worth $35,000. Which one of the following statements is correct concerning their investments? Assume that they will continue earning the same rate of return.
A.Two years from now, Max’s investment will be worth more than Julie’s.
B. Last year, Julie’s investment was worth more than Max’s.
C. Max has earned more interest on interest than Julie.
D. Julie has earned an average annual interest rate of 6.7%.
E. Max has earned an average annual interest rate of 6.41%.

Fred and Max each want to have $10,000 saved five years from now. Fred can earn 4.35%, compounded annually, on his savings and Max can earn 4.50%, compounded annually, on his savings. Both Fred and Max are going to deposit one lump sum today and will not add any additional funds to their accounts. Given this, Max _____ deposit _____ Fred to achieve the goal.
A.Must; more than
B. Must; at least as much as
C. Must; as much or more than
D. Can; less than
E. Can; the same amount as

Nadine invests $1,000 at 8% when she is 25 years old. Neal invests $1,000 at 8% when he is 40 years old. Both investments compound interest annually. Both Nadine and Neal retire at age 60. Which one of the following statements is correct?
A.Nadine will have less money when she retires than Neal.
B. Neal will earn more interest on interest than Nadine.
C. Neal will earn more compound interest than Nadine.
D. If Neal waits to age 70 to retire, then he will have just as much money as Nadine.
E. Nadine will have more money when she retires than Neal.

Given a constant future value and discount rate, an increase in the number of time periods will _____ the present value.
A.Decrease
B. Either not affect or decrease
C. Not affect
D. Either increase or not affect
E. Increase

Compound interest is best defined as the interest earned:
A.On prior year’s interest which was reinvested.
B. On a simple basis for multiple years.
C. On the initial investment for a stated number of periods.
D. On both the interest reinvested from prior periods and the initial investment.
E. For the first year multiplied by the number of years in the investment period.

Suppose that r and t are greater than zero, which statement is correct?
A.Present value interest factors are less than one.
B. Only Future value interest factors are less than one.
C. Only Present value interest factors are greater than future value interest factors.
D. Only Present value interest factors grow as t grows, provided r is held constant.
E. Present value interest factors are negative.

The value today of future cash flows discounted at the appropriate discount rate is called the _____ value.
A.Principal
B. Future
C. Present
D. Simple
E. Compound

The current value of future cash flows discounted at the appropriate discount rate is called the:
A.Principal value.
B. Future value.
C. Present value.
D. Simple interest rate.
E. Compound interest rate.

All else being the same, which of the following statements is correct?
A.Present values increase as the discount rate increases I only.
B. Present values decrease as the discount rate decreases.
C. Present values increase the further away in time the future value.
D. Present values are always smaller than future values when both r and t are positive.
E. Present values are always smaller than future values when r is negative and t positive.

The current value of future cash flows discounted at the appropriate discount rate to current time is called the _____ value.
A.Principal.
B. Future.
C. Present.
D. Simple.
E. Compound.

The amount an investment is worth after one or more periods of time is the ___________.
A.Future value.
B. Present value.
C. Principal value.
D. Compound interest rate.
E. Simple interest rate.

The formula for a present value calculation using Excel is:
A.PV (rate, nper, pmt, pv).
B. PV (nper, pmt, fv).
C. PV (rate, pmt, pv, fv).
D. PV (rate, nper, pmt, fv).
E. PV (rate, nper, pmt).

The present value equation is:
A.PV = FV_t+ (1 + r)^t.
B. PV = FV_t– (1 + r)^t.
C. PV = FV_t/[1/(1 + r)^t].
D. PV = FV_t/(1 + r)^t.
E. PV = FV_t* (1 + r)^t.

Suppose you are trying to find the present value of two different cash flows using the same interest rate for each. One cash flow is $1,000 ten years from now, the other $800 seven years from now. Which of the following is true about the discount factors used in these valuations?
A.The discount factor for the cash flow ten years away is always less than or equal to the discount factor for the cash flow that is received seven years from now.
B. Both discount factors are greater than one.
C. Regardless of the interest rate, the discount factors are such that the present value of the $1,000 will always be greater than the present value of the $800.
D. Since the payments are different, no statement can be made regarding the discount factors.
E. You should factor in the time differential and choose the payment that arrives the soonest.

Grandma Jenkins knows that she has between six and nine months left to live. She wants to leave each of her grandchildren $1,000 when she dies. For this purpose, she has established a trust fund and has deposited sufficient monies to provide for her twelve grandchildren. Today, she just discovered that her daughter is going to have twins, increasing the number of her grandchildren to thirteen. To ensure her final wish is fully funded, Grandma Jenkins needs to:
A.Withdraw $1,000 from her trust account.
B. Withdraw less than $1,000 from her trust account.
C. See if the rate of interest on her account can be lowered.
D. Deposit at least $1,050 into her trust account.
E. Deposit a little less than $1,000 into her trust account.

Interest earned on both the initial principal and the interest reinvested from prior periods is called ____________.
A.Free interest.
B. Annual interest.
C. Simple interest.
D. Interest on interest.
E. Compound interest.

Interest earned on the reinvestment of previous interest payments is called _____________.
A.Free interest.
B. Annual interest.
C. Simple interest.
D. Interest on interest.
E. Compound interest.

Interest earned only on the original principal amount invested is called _______________.
A.Free interest.
B. Annual interest.
C. Simple interest.
D. Interest on interest.
E. Compound interest.

Interest earned on the reinvestment of previous interest payments is called _____ interest.
A.Free.
B. Annual.
C. Simple.
D. Interest on.
E. Intermediary.

Interest earned only on the original principal amount invested is called _____ interest.
A.Free.
B. Annual.
C. Simple.
D. Interest on.
E. Compound.

Margaret invests at 6% simple interest for six years. Pete invests at 6%, compounded annually, for eight years. Sylvia invests for eight years at 6% simple interest. Which one of the following statements is correct if all three individuals invested the same amount of money on the same day?
A.Margaret will have more money than Sylvia at the end of three years.
B. Pete will have more money than either Margaret or Sylvia at the end of four years.
C. Sylvia will have more money than either Margaret or Pete at the end of six years.
D. Margaret will have less money than Pete but more money than Sylvia at the end of five years.
E. Sylvia and Margaret will have more money than Pete at the end of six years.

Fresh out of college, you are negotiating with your prospective new employer. They offer you a signing bonus of $2,000,000 today or a lump sum payment of $2,500,000 three years from now. If you can earn 7% on your invested funds, which of the following is true?
A.Take the signing bonus because it has the lower present value.
B. Take the signing bonus because it has the higher future value.
C. Take the lump sum because it has the higher present value.
D. Take the lump sum because it has the lower future value.
E. Based on these numbers, you are indifferent between the two.

A customer makes two offers to settle a disputed account. He will either pay you $500 today or pay you $650 in three years. Which one of the following is correct if your company earns 10.5% on its surplus funds?
A.The company should accept the $650 offer as it pays $150 more.
B. The company should accept the $650 offer as it is worth more today.
C. The company should accept the $650 offer as it is worth $12.42 more today.
D. The company should accept the $500 offer as it is worth $18.24 more today.
E. The company should accept the $500 offer as it is worth $512.42 today.

Future value is best defined as:
A.An amount of money received each period for a stated number of periods.
B. The amount an investment is worth in today’s dollars.
C. The dollar amount invested today at a stated rate of interest for some period of time.
D. The amount an investment is worth at the end of some stated period of time.
E. The cash value of an investment in today’s dollars based on a stated rate of interest.

The future value factor will decrease:
A.The longer the period of time.
B. The lower the present value factor.
C. The lower the interest rate.
D. The higher the present value.
E. The higher the future value.

The present value factor will decrease:
A.The longer the period of time.
B. The higher the future value.
C. The lower the interest rate.
D. The higher the present value.
E. The slower the rate of growth.

Many financial calculators require that:
A.The interest rate be input as a decimal, such as.07.
B. Interest be compounded on an annual basis.
C. The present value be input as a negative number when solving for the interest rate.
D. Interest be computed on a monthly basis.
E. Either the present value or the future value be input as a negative number when solving for the number of periods.

Which one of the following statements is correct?
A.The future value decreases as the period of time increases, all else constant.
B. The future value of $100 invested at 6% simple interest increases at a constant rate as the period of time increases.
C. There is an inverse relationship between the future value of a lump sum investment and the length of the investment period.
D. The future value of $100 invested at 6%, compounded annually, increases over time in an exponential manner.
E. Because time is the exponent in the future value formula, the length of an investment period has minimal effect on the future value of the investment.

Tishie invests $3,000 today at a 9% rate of return. She wants to have $24,000 to give to her granddaughter Kathy for college 16 years from now. Which one of the following statements is correct concerning Tishie’s situation?
A.Tishie will have the $24,000 when she wants it.
B. Tishie would have to wait an additional ten years to have $24,000.
C. Tishie would have to earn a 10% rate of return to have $24,000 in 16 years.
D. Tishie will only have approximately $12,000 sixteen years from now.
E. Tishie should plan on only giving Kathy $10,000 in sixteen years.

Accessibility: Keyboard Navigation
Blooms: Understand
Difficulty: Medium
Learning Objective: 05-02 How to determine the present value of cash to be received at a future date.
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-05 Present Value and Discounting
Topic: 05-08 More on Present and Future Values
Topic: 05-09 Present versus Future Value

Present value is defined as the:
A.Amount of money invested each time period for a stated number of periods.
B. Summation of the cash flows received within a specified period of time.
C. Value of future cash flows in today’s dollars given a specific discount rate.
D. Compounded value of a principal amount given a specific rate of interest.
E. Value of an investment given simple interest for a specific period of time.

Seven years ago David deposited $10,000 into an account earning 5.25% compounded monthly. Recently, David was quoted by a home improvement firm a price of $15,000 to renovate his roof. Does David have enough cash on hand to pay for the roof?
A.Yes. David now has exactly $15,000 in his account.
B. No. David has only $14,430 in his account.
C. Yes. David now has $17,818 in his account.
D. No. David has $12,818 in his account
E. No. David has only $11,508 in his account

Which one of the following statements is correct if you invest $100 in an account at a simple interest rate of 4% for five years?
A.You will earn more interest than if you invested in an account which compounded the interest.
B. For every $1 you earn in interest in the first year, you will earn ($1.04) interest in the second year.
C. You will earn interest on interest for four of the five years.
D. The amount of interest you earn in year five will equal the interest you earn in year one, whether or not you reinvest your earnings.
E. The total interest you will earn over five years will be equal to $100 x (1 +.04)^5.

Short Answer Questions

Provide a graphical illustration of future value over a ten year time span given rates of return of 0%, 5%, 10%, 15% and 20%.

Blooms: Analyze
Difficulty: Medium
Learning Objective: 05-01 How to determine the future value of an investment made today.
Topic: 05-01 Future Value and Compounding

If $10,000 was invested at 4% over ten years, determine the difference if this investment was based on simple interest versus interest that was compounded annually.

Simple interest provides a future value of $14,800, while compounded annually provides $14,802.44.

Accessibility: Keyboard Navigation
Blooms: Apply
Difficulty: Medium
Learning Objective: 05-01 How to determine the future value of an investment made today.
Topic: 05-01 Future Value and Compounding

If $20,000 was invested at 5% over five years, determine the difference if this investment was based on simple interest versus interest that was compounded annually.

Simple interest provides a future value of $25,000, while compounded annually provides $25,525.63.

Accessibility: Keyboard Navigation
Blooms: Apply
Difficulty: Medium
Learning Objective: 05-01 How to determine the future value of an investment made today.
Topic: 05-01 Future Value and Compounding

Provide a definition of time value of money.

Refers to the fact that a dollar today is worth more than a dollar at a future point in time, given positive rates of interest.

Provide a definition of compound interest.

Interest earned on both the initial principal and the interest reinvested from prior periods.

What is the difference in future value if $20,000 is invested at 5% over ten years, with one option compounding interest semi-annually, while the other is based on quarterly compounding?

Semi-annual compounding provides a return of $32,772.33, while quarterly compounding provides a return of $32,872.39, for a difference of $100.06.

What is the difference in future value if $40,000 is invested at 5% over twenty years, with one option compounding interest annually, while the other is based on monthly compounding?

Annual compounding provides a return of $106,131.91, while monthly compounding provides a return of $108,505.61 for a difference of $2,373.70.

Provide a definition of compounding.

The process of reinvesting interest earned on the investment such that it accumulates interest.

Provide a definition of simple interest.

Interest earned only on the original principal amount invested.

Provide a definition of interest on interest.

Interest earned on the reinvestment of previous interest payments.

Provide a definition of future value (FV).

The amount an investment is worth after one or more periods. Also compound value.

Provide a definition of discount rate.

The rate used to calculate the present value of future cash flows.

Provide a definition of discount.

To calculate the present value of some future amount.

Susie and Tim are twins. Susie invests $5,000 at age 20 and earns 5% compound interest. Tim invests $10,000 at age 40 and earns 5% compound interest. No matter how long they live, Tim will never have as much money as Susie. Explain why.

By age 40, Susie’s funds had grown to $13,266.49, which is more than the amount of money Tim is investing at that point in time. The key here is time. Time is the exponential function and therefore has a tremendous impact on the value of money. Even though Tim invests twice as much money, he will always have less than Susie.

Explain what compounding is and the relationship between compound interest earned and the number of years over which an investment is compounded.

Compounding is earning interest on interest. Compounding is not very significant over short time periods, but greatly increases in importance over a longer time period.

Accessibility: Keyboard Navigation
Blooms: Remember
Difficulty: Easy
Learning Objective: 05-01 How to determine the future value of an investment made today.
Topic: 05-01 Future Value and Compounding

Why do you think the concept known as the time value of money plays such a critical role in finance?

Student answers will vary. However, each response should demonstrate (1) an understanding that $1 today is worth more than $1 tomorrow and (2) that all investment decisions should consider the impact of this concept.

Accessibility: Keyboard Navigation
Blooms: Analyze
Difficulty: Easy
Learning Objective: 05-01 How to determine the future value of an investment made today.
Topic: 05-01 Future Value and Compounding

Explain what compounding is and the relationship between compound interest earned and the number of years over which an investment is compounded.

Compounding is earning interest on interest. Compounding is not significant over short time periods, but increases in importance the longer the time period considered.

Accessibility: Keyboard Navigation
Blooms: Understand
Difficulty: Easy
Learning Objective: 05-01 How to determine the future value of an investment made today.
Topic: 05-04 A Note on Compound Growth

Provide a graphical illustration of present value over a twenty year time span given rates of return of 0%, 5%, 10%, 15% and 20%.

Blooms: Analyze
Difficulty: Medium
Learning Objective: 05-02 How to determine the present value of cash to be received at a future date.
Topic: 05-05 Present Value and Discounting

Provide a definition of present value (PV).

The current value of future cash flows discounted at the appropriate discount rate.

Explain intuitively why it is that present values decrease as the discount rate increases.

Intuitively, a dollar today is worth more than a dollar tomorrow. As a practical matter, the discount rate is an opportunity cost, and the higher the rate, the higher the cost.

You are considering two lottery payment streams. Choice A pays $1,000 today and choice B pays $1,750 at the end of five years from now. Using a discount rate of 5%, based on present values, which would you choose? Using the same discount rate of 5%, based on future values, which would you choose? What do your results suggest as a general rule for approaching such problems? (Make your choices based purely on the time value of money.)

PV of A = $1,000; PV of B = $1,371; FV of A = $1,276; FV of B = $1,500. Based on both present values and future values, B is the better choice. The student should recognize that finding present values and finding future values are simply reverse processes of one another, and that choosing between two lump sums based on PV will always give the same result as choosing between the same two lump sums based on FV.

Accessibility: Keyboard Navigation
Blooms: Evaluate
Difficulty: Medium
Learning Objective: 05-02 How to determine the present value of cash to be received at a future date.
Topic: 05-05 Present Value and Discounting

Present value is used extensively by managers who are reviewing proposed projects. How does the present value of a cash flow assist management in making these business decisions?

By converting cash flows into present values, management can compare and contrast various alternative opportunities and determine which course of action is best for the firm. The present value allows management to view projects on an equivalent basis. Also, by knowing the present value of the future cash flows of a project, management can determine if those cash inflows are sufficient to offset the required investment in the project. While students may have various answers, this question starts them thinking about financial decision-making, which is covered later in the text.

Write a sentence explaining why present values decrease as the discount rate increases.

Student answers will vary. Here is one example. When you can earn more interest, you need less of your own money to reach the same future dollar amount.

You wish to have $200,000 at the end of twenty years. In the last five years, you withdraw $1,000 annually at a rate of 3.8% compounded quarterly. During the middle ten years, you contribute $500 monthly at a rate of 2.8% compounded semi-annually. Given this information, determine the initial deposit that has to be made at the start of the first five years at a rate of 4% compounded monthly.

The initial deposit will be $9,056.50.

You wish to have $400,000 at the end of twenty-five years. In the last ten years, you contribute $1,000 semi-annually at a rate of 5.8% compounded monthly. During the middle ten years, you withdraw $750 quarterly at a rate of 4.5% compounded annually. Given this information, determine the initial deposit that has to be made at the start of the first five years at a rate of 4% compounded monthly.

The initial deposit will be $130,150.00.

Define and explain the relationship between the present value and the discount rate. Graphically illustrate this relationship.

The present value is inversely related to the discount rate. If you can earn more interest, then it takes less of an initial investment to reach a predetermined future value. Students should draw a graph depicting an inverse relationship.

An investor is considering depositing $20,000 in an account earning 5% compounded quarterly for the next three years. Afterwards, he will take this amount and contribute $200 quarterly for the next four years at a rate of 4% compounded semi-annually. Finally, over the next two years, he will withdraw $1,000 annually at a rate of 3.5% compounded monthly. Determine the future value at the end of this time period.

The future value will be $30,833.94.

An investor is considering depositing $10,000 in an account earning 3% compounded monthly for the next two years. Afterwards, he will take this amount and contribute $500 monthly for the next three years at a rate of 5% compounded annually. Finally, over the next three years, he will withdraw $500 annually at a rate of 4.5% compounded semi-annually. Determine the future value at the end of this time period.

The future value will be $34,584.92

The notion that money has “time-value” is based on the existence of a nonzero “opportunity rate”, i.e., a rate of return at which it is possible to invest. Why is the opportunity rate so important?

We have found that, while they are able to perform compounding and discounting computations successfully, some students never really grasp the “why” of the computation. This question is designed to probe the issue of “why time value procedures work” more deeply. An adequate answer will indicate that the opportunity rate is the rate of return that equates two different dollar values at two different points in time. That is, a rational investor will be indifferent to $.9091 today and $1.00 in one year.

An investor is considering depositing $10,000 and making $400 semi-annual contributions for the next five years. If one investment provides 5% compounded monthly and another investment provides 5.2% compounded semi-annually, determine the difference between the two investments.

The investment earning 5% will have a future value of $17,320.33, while the investment earning 5.2% will have a future value of $17,428.25, for a difference of $107.92.

What is the rate needed (compounded monthly) for $10,000 to mature to $25,000 in 15 years?

The required rate of return is 6.12% compounded quarterly.

What is the rate needed (compounded annually) for $95,000 to mature to $250,000 in 25 years?

The required rate of return is 3.95% compounded monthly.

$15,000 is invested into a plan earning 5% compounded quarterly for the first ten years. What will the rate of interest have to be for the next ten years (compounded monthly) for the value to reach $40,000?

The rate of interest will have to be 4.85%.

An investor is considering depositing $20,000 and making monthly contributions of $250 per month into investment. If the investor wants to have a future value of $50,000, what will be the rate of interest if he wishes to have this amount in 5 years? Assume interest is compounded monthly.

The rate of interest will have to be 8.92%.

Some financial advisors recommend you increase the amount of federal income taxes withheld from your pay cheque each month so that you will get a larger refund come April. That is, you take home less today but get a bigger lump sum when you get your refund. Based on your knowledge of the time value of money, what do you think of this idea? Explain.

Some students may slip in a discussion about the benefits of forced savings, etc., but these issues are based on preferences, not the time value of money. Based on the time value of money, the students should recommend the opposite tack, that is, withhold as little as possible and pay the tax bill when it comes the following year. This is the usual dollar today versus a dollar tomorrow argument. Of course, the astute student will note the potential tax complications of this strategy, namely the CRA penalty for insufficient withholding, but the basic argument still applies.

How long will it take for money to double at a rate of 6% compounded monthly?

At the given rate, money will double in 11 years and 7 months.

How long will it take for money to tripe at a rate of 4.5% compounded quarterly?

At the given rate, money will triple in 24.55 years.

At an interest rate of 10% and using the Rule of 72, how long will it take to double the value of a lump sum invested today? How long will it take after that until the account grows to four times the initial investment? Given the power of compounding, shouldn’t it take less time for the money to double the second time?

It will take 7.2 years to double the initial investment, then another 7.2 years to double it again. That is, it takes 14.4 years for the value to reach four times the initial investment. Compounding doesn’t affect the amount of time it takes for an investment to double the second time, but note that during the first 7.2 years, the interest earned is equal to 100% of the initial investment. During the second 7.2 years, the interest earned is equal to 200% of the initial investment. That is the power of compounding.

Accessibility: Keyboard Navigation
Blooms: Analyze
Difficulty: Medium
Learning Objective: 05-03 How to find the return on an investment and the time it takes for an investment to reach a desired value.
Topic: 05-11 Finding the Number of Periods

State the future value formula and explain the effect that time has on the future value of an investment.

FV = PV(1 + r)^t
Time is the exponential function. Thus, time has a significant bearing on the future value of an investment because the future value rises exponentially in response to time. The longer the time period, the greater this effect will be.

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