Deck 5: Introduction to Valuation: the Time Value of Money

Question 1

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

Answer 1

True

Question 2

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.

Answer 2

True

Question 3

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

Answer 3

False

Question 4

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

Question 5

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

Question 6

Future value is always higher than present value

Question 7

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

Question 8

Present values increase as the discount rate increases.

Question 9

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.

Question 10

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.

Question 11

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

Question 12

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

Question 13

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.

Question 14

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

Question 15

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.

Question 16

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.

Question 17

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

Question 18

Future value can be lower than present value

Question 19

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.

Question 20

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

Question 21

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

Question 22

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.

Question 23

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

Question 24

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

Question 25

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

Question 26

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.

Question 27

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.

Question 28

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

Question 29

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.

Question 30

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

Question 31

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.

Question 32

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

Question 33

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

Question 34

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

Question 35

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

Question 36

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

Question 37

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

Question 38

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

Question 39

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

Question 40

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

Question 41

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

Question 42

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

Question 43

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

Question 44

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

Question 45

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

Question 46

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

Question 47

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

Question 48

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

Question 49

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

Question 50

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

Question 51

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

Question 52

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

Question 53

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

Question 54

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

Question 55

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

Question 56

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

Question 57

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

Question 58

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

Question 59

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

Question 60

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

Question 61

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

Question 62

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

Question 63

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

Question 64

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

Question 65

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

Question 66

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

Question 67

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

Question 68

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

Question 69

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

Question 70

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

Question 71

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

Question 72

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

Question 73

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

Question 74

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

Question 75

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

Question 76

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

Question 77

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

Question 78

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

Question 79

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

Question 80

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