Deck 5: Time Value of Money

Question 1

The future value of $200 received today and deposited at 8 percent for three years is

A) $248.
B) $252.
C) $158.
D) $200.

Answer 1

$252.

Question 2

Everything else being equal, the higher the interest rate, the higher the future value.

Answer 2

True

Question 3

The amount of money that would have to be invested today at a given interest rate over a specified period in order to equal a future amount is called

A) future value.
B) present value.
C) future value of an annuity.
D) present value of an annuity.

Answer 3

present value.

Question 4

Calculate the present value of $89,000 to be received in 15 years, assuming an opportunity cost of 14 percent.

Question 5

The future value of a dollar ________ as the interest rate increases and ________ the farther in the future an initial deposit is to be received.

A) decreases; decreases
B) decreases; increases
C) increases; increases
D) increases; decreases

Question 6

The present value of $100 to be received 10 years from today, assuming an opportunity cost of 9 percent, is

A) $236.
B) $699.
C) $ 42.
D) $ 75.

Question 7

Everything else being equal, the longer the period of time, the lower the present value.

Question 8

The future value of $100 received today and deposited at 6 percent for four years is

A) $126.
B) $ 79.
C) $124.
D) $116.

Question 9

Future value increases with increases in the interest rate or the period of time funds are left on deposit.

Question 10

The greater the interest rate and the longer the period of time, the higher the present value.

Question 11

The present value of $200 to be received 10 years from today, assuming an opportunity cost of 10 percent, is

A) $ 50.
B) $200.
C) $518.
D) $ 77.

Question 12

Everything else being equal, the higher the discount rate, the higher the present value.

Question 13

If you expect to retire in 30 years, are currently comfortable living on $50,000 per year and expect inflation to average 3% over the next 30 years, what amount of annual income will you need to live at the same comfort level in 30 years?

A) $121,363
B) $95,000
C) $20,599
D) $51,500

Question 14

The annual rate of return is variously referred to as the

A) discount rate.
B) opportunity cost.
C) cost of capital.
D) all of the above.

Question 15

Calculate the future value of $4,600 received today if it is deposited at 9 percent for three years.

Question 16

Future value is the value of a future amount at the present time, found by applying compound interest over a specified period of time.

Question 17

When the amount earned on a deposit has become part of the principal at the end of a specified time period the concept is called

A) discount interest.
B) compound interest.
C) primary interest.
D) future value.

Question 18

For a given positive interest rate, the future value of $100 increases with the passage of time. Thus, the longer the period of time, the greater the future value.

Question 19

Since individuals are always confronted with opportunities to earn positive rates of return on their funds, the timing of cash flows does not have any significant economic consequences.

Question 20

Time-value of money is based on the belief that a dollar that will be received at some future date is worth more than a dollar today.

Question 21

Indicate which of the following is true about annuities.

A) An ordinary annuity is an equal payment paid or received at the beginning of each period.
B) An annuity due is a payment paid or received at the beginning of each period that increases by an equal amount each period.
C) An annuity due is an equal payment paid or received at the beginning of each period.
D) An ordinary annuity is an equal payment paid or received at the end of each period that increases by an equal amount each period.

Question 22

Dan and Jia are newlyweds and have just purchased a condominium for $70,000. Since the condo is very small, they hope to move into a single-family house in 5 years. How much will their condo worth in 5 years if inflation is expected to be 8 percent?

Question 23

Bill plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 20 years. If Bill can earn 12 percent on his contributions, how much will he have at the end of the twentieth year?

A) $19,292
B) $14,938
C) $40,000
D) $144,104

Question 24

The future value of a $10,000 annuity due deposited at 12 percent compounded annually for each of the next 5 years is

A) $36,050.
B) $63,530.
C) $40,376.
D) $71,154.

Question 25

The present value of a $20,000 perpetuity at a 7 percent discount rate is

A) $186,915.
B) $285,714.
C) $140,000.
D) $325,000.

Question 26

An annuity with an infinite life is called a(n)

A) perpetuity.
B) primia.
C) indefinite.
D) deep discount.

Question 27

The present value of a $25,000 perpetuity at a 14 percent discount rate is

A) $178,571.
B) $285,000.
C) $350,000.
D) $219,298.

Question 28

The future value of an ordinary annuity of $2,000 each year for 10 years, deposited at 12 percent, is

A) $35,098.
B) $20,000.
C) $39,310.
D) $11,300.

Question 29

Colin has inherited $6,000 from the death of Grandma Anna. He would like to use this money to buy his mom Hayley a new scooter costing $7,000 2 years from now. Will Colin have enough money to buy the gift if he deposits his money in an account paying 8 percent compounded semi-annually?

Question 30

In comparing an ordinary annuity and an annuity due, which of the following is true?

A) The future value of an annuity due is always greater than the future value of an otherwise identical ordinary annuity.
B) The future value of an ordinary annuity is always greater than the future value of an otherwise identical annuity due.
C) The future value of an annuity due is always less than the future value of an otherwise identical ordinary annuity, since one less payment is received with an annuity due.
D) All things being equal, one would prefer to receive an ordinary annuity compared to an annuity due.

Question 31

An ordinary annuity is an annuity in which cash flows occurs at the beginning of each period.

Question 32

The future value of an ordinary annuity of $1,000 each year for 10 years, deposited at 3 percent, is

A) $11,808.
B) $11,464.
C) $ 8,530.
D) $10,000.

Question 33

________ is an annuity with an infinite life making continual annual payments.

A) An amortized loan
B) A principal
C) A perpetuity
D) An APR

Question 34

China Manufacturing Agents, Inc. is preparing a five-year plan. Today, sales are $1,000,000. If the growth rate in sales is projected to be 10 percent over the next five years, what will the dollar amount of sales be in year five?

Question 35

An annuity due is an amount that occurs at the beginning of each period.

Question 36

Congratulations! You have just won the lottery! However, the lottery bureau has just informed you that you can take your winnings in one of two ways. Choice X pays $1,000,000. Choice Y pays $1,750,000 at the end of five years from now. Using a discount rate of 5 percent, based on present values, which would you choose? Using the same discount rate of 5 percent, 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.)

Question 37

Dan plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 10 years. If Dan can earn 10 percent on his contributions, how much will he have at the end of the tenth year?

A) $12,290
B) $20,000
C) $31,874
D) $51,880

Question 38

The future value of a $2,000 annuity due deposited at 8 percent compounded annually for each of the next 10 years is

A) $28,974.
B) $31,292.
C) $14,494.
D) $13,420.

Question 39

Aunt Tillie has deposited $33,000 today in an account which will earn 10 percent annually. She plans to leave the funds in this account for seven years earning interest. If the goal of this deposit is to cover a future obligation of $65,000, what recommendation would you make to Aunt Tillie?

Question 40

The future value of an annuity due is always greater than the future value of an otherwise identical ordinary annuity for interest rates greater than zero.

Question 41

The present value of an ordinary annuity of $350 each year for five years, assuming an opportunity cost of 4 percent, is

A) $288.
B) $1,896.
C) $1,750.
D) $1,558.

Question 42

Calculate the present value of a $10,000 perpetuity at a 6 percent discount rate.

Question 43

Jia has just won a $20 million lottery, which will pay her $1 million at the end of each year for 20 years. An investor has offered her $10 million for this annuity. She estimates that she can earn 10 percent interest, compounded annually, on any amounts she invests. She asks your advice on whether to accept or reject the offer. What will you tell her? (Ignore Taxes)

Question 44

To pay for her college education, Gina is saving $2,000 at the beginning of each year for the next eight years in a bank account paying 12 percent interest. How much will Gina have in that account at the end of 8th year?

A) $16,000
B) $17,920
C) $24,600
D) $27,552

Question 45

Nico establishes a seven-year, 8 percent loan with a bank requiring annual end-of-year payments of $960.43. Calculate the original principal amount.

Question 46

The present value of an ordinary annuity of $2,350 each year for eight years, assuming an opportunity cost of 11 percent, is

A) $ 1,020.
B) $27,869.
C) $18,800.
D) $12,093.

Question 47

A generous philanthropist plans to make a one-time endowment to a renowned heart research center which would provide the facility with $250,000 per year into perpetuity. The rate of interest is expected to be 8 percent for all future time periods. How large must the endowment be?

A) $2,314,814
B) $2,000,000
C) $3,125,000
D) $3,000,000

Question 48

You have been offered a project paying $300 at the beginning of each year for the next 20 years. What is the maximum amount of money you would invest in this project if you expect 9 percent rate of return to your investment?

A) $ 2,738.70
B) $ 2,985.18
C) $15,347.70
D) $ 6,000.00

Question 49

Mary will receive $12,000 per year for the next 10 years as royalty for her work on a finance book. What is the present value of her royalty income if the opportunity cost is 12 percent?

A) $120,000
B) $ 67,800
C) $ 38,640
D) None of the above.

Question 50

Dottie has decided to set up an account that will pay her granddaughter (Lexi) $5,000 a year indefinitely. How much should Dottie deposit in an account paying 8 percent annual interest?

Question 51

Calculate the future value of an annuity of $5,000 each year for eight years, deposited at 6 percent.

Question 52

In their meeting with their advisor, Mr. and Mrs. O'Rourke concluded that they would need $40,000 per year during their retirement years in order to live comfortably. They will retire 10 years from now and expect a 20-year retirement period. How much should Mr. and Mrs. O'Rourke deposit now in a bank account paying 9 percent to reach financial happiness during retirement?

Question 53

Mr. Knowitall has been awarded a bonus for his outstanding work. His employer offers him a choice of a lump-sum of $5,000 today, or an annuity of $1,250 a year for the next five years. Which option should Mr. Knowitall choose if his opportunity cost is 9 percent?

Question 54

A wealthy industrialist wishes to establish a $2,000,000 trust fund which will provide income for his grandchild into perpetuity. He stipulates in the trust agreement that the principal may not be distributed. The grandchild may only receive the interest earned. If the interest rate earned on the trust is expected to be at least 7 percent in all future periods, how much income will the grandchild receive each year?

Question 55

James plans to fund his individual retirement account, beginning today, with 20 annual deposits of $2,000, which he will continue for the next 20 years. If he can earn an annual compound rate of 8 percent on his deposits, the amount in the account upon retirement will be

A) $19,636.
B) $91,524.
C) $98,846.
D) $21,207.

Question 56

A lottery administrator has just completed the state's most recent $50 million lottery. Receipts from lottery sales were $50 million and the payout will be $5 million at the end of each year for 10 years. The expenses of running the lottery were $800,000. The state can earn an annual compound rate of 8 percent on any funds invested.
(a) Calculate the gross profit to the state from this lottery.
(b) Calculate the net profit to the state from this lottery (no taxes).

Question 57

A generous benefactor to the local ballet plans to make a one-time endowment which would provide the ballet with $150,000 per year into perpetuity. The rate of interest is expected to be 5 percent for all future time periods. How large must the endowment be?

A) $ 300,000
B) $3,000,000
C) $ 750,000
D) $1,428,571

Question 58

A college received a contribution to its endowment fund of $2 million. They can never touch the principal, but they can use the earnings. At an assumed interest rate of 9.5 percent, how much can the college earn to help its operations each year?

A) $95,000
B) $19,000
C) $190,000
D) $18,000

Question 59

If the present value of a perpetual income stream is increasing, the discount rate must be

A) increasing.
B) decreasing.
C) changing unpredictably.
D) increasing proportionally.

Question 60

Calculate the present value of an annuity of $3,900 each year for four years, assuming an opportunity cost of 10 percent.

Question 61

Find the future value at the end of year 3 of the following stream of cash flows received at the end of each year, assuming the firm can earn 8 percent on its investments.

A) $45,000
B) $53,396
C) $47,940
D) $56,690

Question 62

Ashley is planning to attend college when she graduates from high school 7 years from now. She anticipates that she will need $10,000 at the beginning of each college year to pay for tuition and fees, and have some spending money. Ashley has made an arrangement with her father to do the household chores if her dad deposits $3,500 at the end of each year for the next 7 years in a bank account paying 8 percent interest. Will there be enough money in the account for Ashley to pay for her college expenses? Assume the rate of interest stays at 8 percent during the college years.

Question 63

$100 is received at the beginning of year 1, $200 is received at the beginning of year 2, and $300 is received at the beginning of year 3. If these cash flows are deposited at 12 percent, their combined future value at the end of year 3 is ________.

A) $1,536
B) $ 672
C) $ 727
D) $1,245

Question 64

Find the present value of the following stream of cash flows, assuming that the firm's opportunity cost is 9 percent.

A) $ 13,252
B) $141,588
C) $ 10,972
D) $ 79,348

Question 65

Calculate the present value of $800 received at the beginning of year 1, $400 received at the beginning of year 2, and $700 received at the beginning of year 3, assuming an opportunity cost of 9 percent.

Question 66

Find the present value of the following stream of cash flows, assuming that the firm's opportunity cost is 25 percent.

A) $27,168
B) $35,200
C) $34,000
D) $32,500

Question 67

Nico is 30 years old and will retire at age 65. He will receive retirement benefits but the benefits are not going to be enough to make a comfortable retirement life for him. Nico has estimated that an additional $25,000 a year over his retirement benefits will allow him to have a satisfactory life. How much should Nico deposit today in an account paying 6 percent interest to meet his goal? Assume Nico will have 15 years of retirement.

Question 68

The present value of $1,000 received at the end of year 1, $1,200 received at the end of year 2, and $1,300 received at the end of year 3, assuming an opportunity cost of 7 percent, is

A) $2,500.
B) $3,043
C) $6,516.
D) $2,856.

Question 69

Last Christmas, Danny received an annual bonus of $1,500. These annual bonuses are expected to grow by 5 percent for the next 5 years. How much will Danny have at the end of the fifth year if he invests his Christmas bonuses (including the most recent bonus) in a project paying 8 percent per year?

Question 70

You are considering the purchase of new equipment for your company and you have narrowed down the possibilities to two models which perform equally well. However, the method of paying for the two models is different. Model A requires $5,000 per year payment for the next five years. Model B requires the following payment schedule. Which model should you buy if your opportunity cost is 8 percent?

Question 71

During her four years at college, Hayley received the following amounts of money at the end of each year from her grandmother. She deposited her money in a saving account paying 6 percent rate of interest. How much money will Hayley have on graduation day?

Question 72

Find the present value of the following stream of cash flows, assuming that the firm's opportunity cost is 14 percent.

A) $131,065
B) $ 19,830
C) $ 14,850
D) $120,820

Question 73

You have provided your friend with a service worth $8,500. Your friend offers you the following cash flow instead of paying $8,500 today. Should you accept his offer if your opportunity cost is 8 percent?

Question 74

You have been given a choice between two retirement policies as described below.
Policy A: You will receive equal annual payments of $10,000 beginning 35 years from now for 10 years.
Policy B: You will receive one lump-sum of $100,000 in 40 years from now.
Which policy would you choose? Assume rate of interest is 6 percent.

Question 75

Find the present value of the following stream of cash flows, assuming that the firm's opportunity cost is 14 percent.

A) $121,256
B) $ 69,000
C) $ 60,513
D) $ 51,885

Question 76

$1,200 is received at the beginning of year 1, $2,200 is received at the beginning of year 2, and $3,300 is received at the beginning of year 3. If these cash flows are deposited at 12 percent, their combined future value at the end of year 3 is ________.

A) $ 6,700
B) $17,000
C) $12,510
D) $ 8,141

Question 77

Calculate the combined future value at the end of year 3 of $1,000 received at the end of year 1, $3,000 received at the end of year 2, and $5,000 received at the end of year 3, all sums deposited at 5 percent.

Question 78

Calculate the present value of $5,800 received at the end of year 1, $6,400 received at the end of year 2, and $8,700 at the end of year 3, assuming an opportunity cost of 13 percent.

Question 79

The present value of $100 received at the end of year 1, $200 received at the end of year 2, and $300 received at the end of year 3, assuming an opportunity cost of 13 percent, is

A) $ 453.
B) $ 416.
C) $1,181.
D) $ 500.

Question 80

Find the future value at the end of year 3 of the following stream of cash flows received at the end of each year, assuming the firm can earn 17 percent on its investments.

A) $20,724
B) $20,127
C) $23,550
D) $23,350