Deck 5: Time Value of Money

Question 1

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

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

Answer 1

$126

Question 2

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

Answer 2

False

Question 3

A certain investment that costs $10,000 today promises to pay you $10,500 in five years.This investment ________.

A)is unambiguously a good investment
B)is unambiguously a bad investment
C)may be a good investment if the rate of return you can earn an alternative investments is very low
D)may be a good investment if the rate of return you can earn on alternative investments is very high

Answer 3

may be a good investment if the rate of return you can earn an alternative investments is very low

Question 4

The 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 5

For any 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 6

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

Question 7

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

Question 8

The main idea behind the time value of money is that a dollar today is worth more than a dollar in the future because ________.

A)inflation erodes the value of money over time
B)investors can earn a return on money they have today and thereby have more money in the future
C)the future is more uncertain than the present
D)investors are impatient

Question 9

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

A)$248
B)$252
C)$159
D)$253

Question 10

The future value of a dollar ________ as the interest rate increases and ________ the longer the money remains invested.

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

Question 11

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

Question 12

You invest a certain amount of money today.The process of determining how much money that investment will produce in the future is called ________.

A)discounting
B)compounding
C)present value
D)annuitizing the cash flow

Question 13

________ is the amount earned on a deposit that has become the part of the principal at the end of a specified time period.

A)Discount interest
B)Compound interest
C)Primary interest
D)Future value

Question 14

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

Question 15

The process of taking cash flow that is received or paid in the future and stating that cash flow in present value terms is called discounting.

Question 16

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

Question 17

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)compounded value

Question 18

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

A)$237
B)$190
C)$42
D)$10

Question 19

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

A)$50
B)$400
C)$519
D)$77

Question 20

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 21

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

A)perpetuity
B)primia
C)option
D)deep discount

Question 22

The annual rate of return is referred to as the ________.

A)discount rate
B)marginal rate
C)risk-free rate
D)marginal cost

Question 23

An annuity due is a stream of equal cash flows with each cash flow arriving at the beginning of each period.

Question 24

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

Question 25

A(n)________ is an annuity with an infinite life making continual annual payments.

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

Question 26

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.You can elect to receive a payment of $1,000,000 now or a payment of $1,750,000 in five years.Assume you can earn 5% on funds that you invest today.How much money would you have in five years if you take the immediate $1,000,000 payment and invest it? What does this tell you about the wisdom of selecting the immediate payment versus the future payment? Using the same 5% interest rate,what is the present value of the $1,750,000 that you could receive in five years? What does this calculation tell you about which lottery payout option you should 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 27

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

Question 28

Dan and Jia are 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 be worth in 5 years if inflation is expected to be 8 percent?

Question 29

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 present 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 30

Colin has inherited $6,000 from his grandmother.He would like to invest this money for two years and then use the proceeds from that investment to buy a new high-end gaming computer for $7,000.Will Colin have enough money to buy the computer if he deposits his money in an account paying 8 percent compounded semiannually?

Question 31

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 32

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 33

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 34

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

Question 35

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 36

Which of the following is TRUE of 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 stream of cash flows that is 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 37

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 38

Bill plans to fund his individual retirement account (IRA)by contributing $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)$19,293
B)$14,939
C)$40,000
D)$144,105

Question 39

Your current income is $50,000 per year,and you would like to maintain your current standard of living (i.e.,your purchasing power)when you retire.If you expect to retire in 30 years 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 40

Dan plans to fund his individual retirement account (IRA)by contributing $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)$12,289
B)$20,000
C)$31,875
D)$51,880

Question 41

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

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

Question 42

A generous benefactor to a local ballet plans to make a one-time endowment that 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 43

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

Question 44

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

Question 45

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 46

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

Question 47

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

A)$35,097
B)$12,656
C)$39,309
D)$11,300

Question 48

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

Question 49

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)$11,128
B)$9,935
C)$24,599
D)$27,551

Question 50

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)$63,528
C)$40,376
D)$71,152

Question 51

The present value of a perpetual income stream increases when the discount rate ________.

A)increases
B)decreases
C)changing unpredictably
D)increasing proportionally

Question 52

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)$2,739
B)$2,985
C)$15,348
D)$16,729

Question 53

A college received a contribution to its endowment fund of $2 million.It can never touch the principal,but 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 54

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 55

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

A)$28,973
B)$31,291
C)$14,494
D)$13,420

Question 56

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)$8,786.

Question 57

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

A)$1,620
B)$1,896
C)$1,971
D)$1,558

Question 58

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

Question 59

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

A)$30,935
B)$27,870
C)$13,424
D)$12,093

Question 60

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? Assume that payments come at the end of each year.

A)$235,855
B)$67,803
C)$210,585
D)$75,939

Question 61

A perpetuity will pay you $100 starting next year and continuing at that level forever.The appropriate discount rate for the perpetuity is 10%.Calculate the present value of (1)the infinite stream of payments,i.e.,the entire perpetuity,and (2)the first 20 payments.Compare these two present values and comment on what they can tell you about the present value of the perpetuity's payments in the very distant future (i.e.,payments made later than 20 years in the future).

Question 62

Mr.Jackson 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.Jackson choose if his opportunity cost is 9 percent?

Question 63

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.Assume that he withdraws $25,000 at the end of each year during retirement.

Question 64

Ashley is planning to attend college when she graduates from high school 7 years from now.She anticipates that she will need $20,000 at the beginning of each of the four college years to pay for tuition and fees,and have some spending money (i.e.,she needs to be able to withdraw $20,000 from savings four times,with the first withdrawal taking place 7 years from now).Ashley's father has promised to help her save for college by making 7 deposits of $7,000 each into an investment accounting earning 8 percent interest.His first payment comes a year from today.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 65

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 66

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? Assume that once they retire,the O'Rourkes will withdraw $40,000 from their retirement account at the end of each year.

Question 67

You inherited an investment portfolio worth $1 million.The portfolio earns a return of 9% per year.You want to withdraw money from this portfolio once per year starting one year from today,and you want to continue making withdrawals forever.Furthermore,you want to increase your withdrawals at 3% per year to keep up with inflation.How large can your first withdrawal be?

Question 68

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 69

You receive $1,200 today,$2,200 in one year,and $3,300 in two years.If you deposit these cash flows in an account earning 12%,how much money is in the account three years from now?

A)$6,221
B)$5,554
C)$7,269
D)$8,142

Question 70

A wealthy benefactor wants to make a donation to a charity that will provide the charity with annual income of $250,000 forever,with the first payment to the charity made exactly 10 years from today.Assume that money donated to the charity will be invested in an account that earns 6%.How large must the donation be to generate the desired income stream?

Question 71

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)$16,320
B)$20,127
C)$23,548
D)$27,551

Question 72

How much money would you have to deposit today to create an income stream that pays $10,000 one year from today and continues to make annual payments forever,with payments after the first $10,000 growing at 4% per year? Assume money that you invest today to fund this income stream earns a 7% rate of return.

A)$142,857
B)$250,000
C)$1,250,000
D)$333,333

Question 73

A university has $16,000,000 invested in its endowment.The university wants to withdraw $800,000 from this endowment starting next year and continuing at annual intervals forever,with each subsequent payment growing at 4% per year.What rate of return does the endowment have to earn to sustain the desired withdrawals?

Question 74

A certain investment promises to pay you $2,500 per year forever with the first payment starting next year.If you can earn a 5% return on similar investments,what's the most you would pay for this investment today?

A)$50,000
B)$5,000
C)$41,667
D)$62,500

Question 75

You receive $1,000 in 1 year,$1,200 in 2 years,and $1,300 in 3 years.The present value today of these future receipts is ________ if the opportunity cost is 7 percent.

A)$2,500
B)$3,044
C)$4,036
D)$3,257

Question 76

A certain investment promises to pay you $2,500 per year forever with the first payment starting 5 years from now.If you can earn a 5% return on similar investments,what's the most you would pay for this investment today?

A)$50,000
B)$39,176
C)$41,135
D)$37,311

Question 77

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 78

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)$51,780
B)$39,248
C)$47,944
D)$40,981

Question 79

You receive $100 today,$200 in one year,and $300 in two years.If you deposit these cash flows into an account earning 12 percent,the value in the account three years from now is ________.

A)less than $600
B)$649
C)$727
D)$815

Question 80

A charitable foundation has $500,000 invested in an account that earns 7%.The foundation has promised to begin making annual payments to beneficiaries in one year,and the first payment will be $25,000.The foundation has promised that future payments will grow at a constant rate forever.At what rate can the foundation afford to increase payments assuming that it makes no additional deposits into the account?

A)0%; it can't afford to increase payments forever without adding more money to the account.
B)1%
C)2%
D)3%