Deck 4: Time Value of Money - Streams and Valuations

Question 1

Bill plans to fund his individual retirement account (IRA)with a 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 twentieth year? (Round to the nearest whole dollar)

A)$19,292
B)$14,938
C)$40,000
D)$144,105
E)$44,800

Answer 1

$144,105

Question 2

You are 30 years old and you want to retire at age 60 with $1.5 million. You are going to make equal annual deposits into your savings account at the end of each year in order to save up this money. Your savings account pays 8% interest. What amount must you deposit each year?

A)$13,241.15
B)$12,160.93
C)$14,227.80
D)$13,274.34
E)$14,506.85

Answer 2

$13,241.15

Question 3

Dan plans to fund his individual retirement account (IRA)with a 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 tenth year? (Round to the nearest whole dollar)

A)$12,290
B)$20,000
C)$31,875
D)$51,880
E)$27,468

Answer 3

$31,875

Question 4

What is the future value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15% interest rate?

A)$670.44
B)$842.91
C)$1,169.56
D)$1,522.64
E)$1,348.48

Question 5

Gina has planned to start college education in four years from now. To pay for her college education, she has decided to save $1,000 a quarter for the next four years in a bank account paying 12 percent interest (compounded quarterly). How much will she have at the end of fourth year? (Round to the nearest whole dollar)

A)$1,574
B)$19,116
C)$20,157
D)$16,000

Question 6

Assume you are to receive a 20-year annuity with annual payments of $50. The first payment will be received at the end of Year 1, and the last payment will be received at the end of Year 20. You will invest each payment in an account that pays 10%. What will be the value in your account at the end of Year 30?

A)$6,354.81
B)$7,427.83
C)$7,922.33
D)$8,591.00
E)$6,752.46

Question 7

Actively managed mutual funds charge higher management fees than passive funds. Assume that the net return to an active fund (after fees)is 9.5% (0.79% per month)and the net return to a passive fund is 10.5% (0.875% per month). Assume that an investor saves $600 per month (end-of-month)over thirty years. What is the difference in the future value of savings between investing in an active fund and a passive fund?

A)$295,152.00
B)$120,519.40
C)$247,352.36
D)$301,732.21

Question 8

You just won the Sweepstakes and have decided to take your winning in 15 equal payments of $35,000. You decide to save all of this money for your retirement and deposit it into an account that earns 11% per year. What is the amount of your retirement nest egg? (Round to the nearest whole dollar)

A)$1,204,188
B)$1,032,161
C)$1,112,037
D)$557,810
E)$852,225

Question 9

Joe expects to start working immediately after graduation and he is already planning to retire. He wants to retire in twenty-five years and hopes that he will be able to do so comfortably by investing $2,000 at the end of each year throughout this period. If he earns 5% compounded annually, how much will be in his retirement fund in twenty-five years?

A)$95,454.20
B)$54,000.00
C)$169,317.75
D)$102,226.00
E)$76,345.93

Question 10

The future value of a $10,000 annuity deposited at 12 percent compounded annually for each of next 5 years is: (Round to the nearest whole dollar)

A)$36,050
B)$71,154
C)$40,376
D)$63,528

Question 11

Jacquie plans to deposit $3,500 into her savings account for each of the next 5 years, and then $2,000 per year for 5 years after that (all at year end). She anticipates interest rates to be 6% for the next 3 years and then 9% thereafter. How much will she have in the account after the 10 years?

A)$43,593.56
B)$30,427.02
C)$34,367.06
D)$35,164.86
E)$42,954.28

Question 12

You can invest $3,000 at the end of each of the next 20 years into a retirement account paying 10% annual interest. Alternatively, you can enter into a retirement plan with your employer where, for every yearly (end-of-year)payment of $3,000 you make, the firm will contribute $1,500. Your employer's plan will also last for the next 20 years. The firm guarantees a return of 7% on its retirement plan. Which option is better?

A)Invest with your employer
B)Indifferent
C)Invest on your own

Question 13

You are expecting to receive $70 per year at the end of each of the next five years. If you invest the money in account that pays 5%, then how much interest will you earn over the five years? (Round to the nearest whole dollar)

A)$37
B)$18
C)$75
D)$350
E)$387

Question 14

Consider an investor who invests $600 per month (end-of-month)over thirty years in a mutual fund that earns 1% per month. What is the future value of her savings?

A)$2,096,978.48
B)$2,606,514.35
C)$2,159,806.22
D)$2,122,696.21
E)$2,545,722.36

Question 15

Sarah found her dream lakefront home, valued at $250,000. She plans to buy a home just like it when she retires in 15 years. Sarah can earn 11% per year on her investments. The price of the house will increase 3% per year for the next 15 years. How much must she invest at the end of each of the next 15 years to finance the purchase?

A)$11,320.67
B)$7,266.31
C)$8,952.82
D)$10,198.81
E)$12,565.95

Question 16

The future value of an ordinary annuity of $1,000 each year for 10 years, deposited at 3 percent, is: (Round to the nearest whole dollar)

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

Question 17

Joan is diligent and, starting on her 19^th Birthday, she deposits $1,000 in a bank account that pays an interest rate of 10%. She continues to save for six more years culminating on her 25^th birthday. After that birthday she stops saving but leaves her accumulated savings in a bank account for 40 years (to age 65). Roseanne is a partier and doesn't start saving until her 26th birthday, at which time she starts saving $1,000 a year until her 65th birthday. (Assume that Roseanne also earns a rate of 10%.)Who has more at age 65?

A)Roseanne
B)Joan
C)They will have the same amount of money.

Question 18

Actively managed mutual funds charge higher management fees than passive funds. Assume that the net return to an active fund (after fees)is 9.5% (0.79% per month)and the net return to a passive fund is 10.5% (0.875% per month). Consider an investor who invests $600 per month (end-of-month)over thirty years in the passive fund. What is the future value of her savings? Now consider an investor who invests on a monthly basis over thirty years in the active fund. If the active fund investor wants the same future value as the passive fund investor, then how much more must she invest per month?

A)$145.79
B)$150.62
C)$59.86
D)$152.33
E)$167.92

Question 19

Janice would like to send her parents on a cruise for their 25th wedding anniversary. She has priced the cruise at $15,000 and she has 5 years to accumulate this money. How much must Janice deposit annually in an account paying 10 percent interest in order to have enough money to send her parents to cruise? (Round to the nearest whole dollar)

A)$1,862
B)$2,457
C)$3,000
D)$2,234
E)$2,135

Question 20

Tony plans to deposit $1,000 at the end of each of the next three years. If his funds earn 5% compounded annually, how much will he have at the end of three years?

A)$3,150.00
B)$3,175.50
C)$3,152.50
D)$3,500.00
E)$4,310.10

Question 21

The Bentley Azure can be leased for four years for $0 down and 48 monthly payments of $4,000 (due at the beginning of each month). Today is the day that the first payment is due. If, instead, you save the payments in a bank account at the nominal annual rate of 7.5%, then how much money will you have at the end of the fourth year? (Round answer to the nearest whole dollar)

A)$224,498
B)$223,103
C)$221,984
D)$222,768
E)$223,326

Question 22

You want to buy a Nissan 300Z on your 27th birthday. You have priced these cars and found that they currently sell for $25,000. You believe that the price will increase by 10 percent per year until you are ready to buy. You can presently invest to earn 14 percent. If you just turned 20 years old, how much must you invest at the end of each of the next 7 years to be able to purchase the Nissan in 7 years?

A)$8,881.21
B)$4,540.14
C)$4,652.18
D)$4,239.56
E)$5,072.09

Question 23

John wants to have $6,215 in 13 years to buy a Laser 2 sailboat with a spinnaker and trapeze. After he has owned the boat for 15 years he will need $2,500 for hull maintenance. How much must he deposit at the end of each year for the next 13 years to save enough money for the purchase and maintenance? His savings account pays 9%.

A)$300.67
B)$267.61
C)$213.02
D)$270.77
E)$211.68

Question 24

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? (Round up to the nearest whole dollar amount)

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

Question 25

The future value of a $2,000 annuity due deposited at 8 percent compounded annually for each of next 10 years is: (Round to the nearest whole dollar)

A)$28,974
B)$31,291
C)$14,494
D)$13,420

Question 26

Suppose someone offered you your choice of two equally risky annuities, each paying $5,000 per year for 5 years. One is an annuity due, while the other is a regular (or deferred)annuity. If you are a rational wealth maximizing investor, which annuity would you choose?

A)The annuity due
B)The deferred annuity
C)Either one, because as the problem is set up, they have the same present value.
D)Without information about the appropriate interest rate, we cannot find the value of the two annuities, hence we cannot tell which is better.
E)The annuity due; however, if the payments on both were doubled to $10,000, the deferred annuity would be preferred.

Question 27

In future value or present value problems, unless stated otherwise, cash flows are assumed to be:

A)At the end of the time period.
B)At the beginning of the time period.
C)In the middle of the time period.
D)Spread out evenly over a time period.

Question 28

If you buy a factory for $250,000 and the terms are 20% down, the balance to be paid off over 30 years at a 12 percent rate of interest on the unpaid balance, what are the 30 equal annual payments? (Round to the nearest whole dollar)

A)$20,593
B)$31,036
C)$24,829
D)$50,212
E)$6,667

Question 29

Margaret plans to deposit $500 on the first day of each of the next five years, beginning today. If she earns 4% compounded annually, how much will she have at the end of five years?

A)$2,708.16
B)$2,816.49
C)$3,041.63
D)$1,560.80
E)$2,041.63

Question 30

An annuity in which payments are made at the beginning of each period is a(n):

A)Ordinary annuity
B)Annuity due
C)Annuity in arrears
D)Perpetuity

Question 31

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 32

5-year regular annuity has a present value of $1,000, and if the interest rate is 10%, what is the amount of each annuity payment?

A)$240.42
B)$263.80
C)$300.20
D)$315.38
E)$346.87

Question 33

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 34

An ordinary annuity may be defined as:

A)A series of equal payments made at regular intervals that are paid at the beginning of each period.
B)A series of payments, which may or may not be equal in value, that are received at regular intervals at the end of each period.
C)A series of equal payments made any time over the course of a year, extending for a period of several years.
D)Any series of payments that occur in the future.
E)A series of equal payments made at regular intervals that are received at the end of each period.

Question 35

What is the future value of an annuity due that pays $500 per year for each of the next three years if the interest rate is 6%?

A)$1,591.80
B)$1,687.31
C)$546.35
D)$2,123.25
E)$2,250.65

Question 36

James plans to fund his individual retirement account, beginning today, with 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 would be: (Round to the nearest whole dollar)

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

Question 37

Peter will receive $1,200 at the beginning of each of the next seven years. What is the future value of this annuity, assuming the interest rate is 9% compounded annually? (Round to the nearest whole dollar)

A)$1,200
B)$11,041
C)$12,034
D)$13,234
E)$8,400

Question 38

You are saving for your child's university education. It is her 1st birthday today. She will start university just after her 19th birthday. You are going to save $2,000 per year each year starting today and ending on her 18th birthday. If you expect to earn a rate of 5% in the savings account, then how much will you have saved by her 19^th birthday?

A)$56,264.77
B)$59,078.01
C)$61,078.01
D)$64,131,91
E)$54,264.77

Question 39

Betty borrows $50,000 at 10 percent annually compounded interest to be repaid in four equal annual installments. The actual end of year loan payment is: (Round to the nearest whole dollar)

A)$10,774
B)$12,500
C)$14,340
D)$15,774

Question 40

In three years you will begin receiving an annual payment of $600 that will be made for two years. If the annual interest rate is 12%, what will be the balance in your account at the end of the fourth year?

A)$2,025
B)$1,344
C)$1,272
D)$1,200
E)$1,260

Question 41

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 42

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 43

An investor is considering the purchase of 20 acres of land. An analysis indicates that if the land is used for cattle grazing, it will produce a cash flow of $1,000 per year indefinitely. If the investor requires a return of 10% on investments of this type, what is the most he or she should be willing to pay for the land?

A)$1,000
B)$10,000
C)$100,000
D)$150,000
E)$1,000,000

Question 44

Suppose the present value of a 2-year ordinary annuity is $100. If the discount rate is 10%, what must be the annual cash flow?

A)$65.45
B)$82.64
C)$57.62
D)$53.78
E)$79.22

Question 45

The present value of a $20,000 perpetuity at a 7 percent discount rate is: (Round to the nearest dollar)

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

Question 46

Ty was seriously injured in a planking accident. He successfully sued the railway company and was awarded $700,000. The railway cannot afford to pay the lump sum immediately and would prefer to make ten annual payments (at the end of each of the next ten years). If the interest rate is 10%, then what size of payment makes Ty indifferent between the lump-sum and the payments?

A)$113,921.78
B)$70,000.00
C)$73,907.45
D)$109,074.06
E)$102,862.66

Question 47

The present value of a $25,000 perpetuity at a 14 percent discount rate is: (Round to the nearest whole dollar.)

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

Question 48

A perpetuity pays $550 at the end of every month. The PV of the perpetuity is $36,000. What is the monthly periodic rate on the perpetuity?

A)1.53%
B)1.62%
C)1.85%
D)2.04%
E)3.25%

Question 49

Marla borrows $4,500 at 12 percent annually compounded interest to be repaid in four equal annual installments. The actual end of year payment is: (Round to the nearest whole dollar)

A)$942
B)$1,125
C)$1,482
D)$2,641

Question 50

A 10-year ordinary annuity that provides a return of 7% has a present value of $15,000. What are the annual annuity payments?

A)$2,135.66
B)$2,038.02
C)$2,235.44
D)$1,500.00
E)$2,232.84

Question 51

You are offered a perpetuity that will pay you $18,000 per year starting in one year. The seller wants you to pay $300,000 for the perpetuity. If you buy it at that price, what return will you earn?

A)6%
B)5%
C)7%
D)8%
E)9%

Question 52

An annuity with an infinite life is called:

A)A perpetuity
B)A prima
C)An in definite
D)A deep discount

Question 53

A perpetuity pays $550 at the end of every month. The PV of the perpetuity is $36,000. What is the nominal annual rate (APR)on the perpetuity?

A)18.33%
B)9.17%
C)19.96%
D)13.42%
E)15.15%

Question 54

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

A)Amortized loan
B)Principal
C)Perpetuity
D)APR

Question 55

You have just taken out a 30-year mortgage on your new home for $120,000. This mortgage is to be repaid in 360 equal monthly installments. If the stated (nominal)annual interest rate is 14.75 percent, what is the amount of each of the monthly installments? Round to the nearest whole dollar.

A)$1,515
B)$1,472
C)$1,493
D)$1,522
E)$1,440

Question 56

Your pension plan has two alternative payout methods. The first is a lump sum of $300,000 on your 65th birthday. The second is ordinary annuity with the first payment on your 66th birthday and the last payment on your 85th birthday. If the interest rate is 10.5%, then what size annuity payment would equate the value of the two alternatives?

A)$36,447.98
B)$35,911.96
C)$37,059.21
D)$35,237.89
E)$34,687.32

Question 57

You have the opportunity to buy a perpetuity which pays $1,000 annually. Your required rate of return on this investment is 15 percent. You should be essentially indifferent to buying or not buying the investment if it were offered at a price of:

A)$5,000.00
B)$6,000.00
C)$6,666.67
D)$7,500.00
E)$8,728.50

Question 58

A perpetuity pays $550 at the end of every month. The PV of the perpetuity is $36,000. What is the effective interest rate (EIR)on the perpetuity?

A)19.95%
B)18.33%
C)9.17%
D)13.42%
E)15.15%

Question 59

In payment for his help with the construction of Valhalla, Wotan offers Fafner two alternatives. First, he offers $1,260 per year forever (with the first payment in one year). Second, he offers his sister-in-law, Freia (the girl with the golden apples). If Fafner thinks that Freia is worth $12,000 and his required rate of return is 10.5%, which of the following is correct?

A)Freia is more valuable.
B)The perpetuity is more valuable.
C)The two are equal in value. He is indifferent between them.

Question 60

What is the present value of a $50 perpetuity if interest rates are 7%?

A)$1.21
B)$18.12
C)$714.29
D)$3.50
E)$593.23

Question 61

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

A)$2,738
B)$2,985
C)$15,347
D)$6,000

Question 62

South Penn Tracking is financing a new truck with a loan of $10,000 to be repaid in 5 annual end-of-year installments of $2,504.56. What annual interest rate is the company paying?

A)7%
B)8%
C)9%
D)10%
E)11%

Question 63

What is the present value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate?

A)$670.43
B)$842.41
C)$1,169.56
D)$1,348.48
E)$1,522.64

Question 64

You expect to receive $800 at the end of each of the next twenty years. What is the present value of the stream of payments if the interest rate is 12%?

A)$5,975.55
B)$5,892.62
C)$6,049.60
D)$6,054.63
E)$5,619.80

Question 65

Starting one month from now, you would like to withdraw $200 per month from your bank account to pay for your university education. You expect the education (and the withdrawals)to last for the next four years. If the account pays 0.3% interest per month, how much money must you have in your bank account today to support your future needs?

A)$8,928.37
B)$7,157.02
C)$6,711.11
D)$8,794.50
E)$7,263.00

Question 66

What is the present value of an ordinary annuity that pays $1,000 per year over each of the next twenty years if the discount rate is 10%? Round to the nearest whole dollar.

A)$8,364
B)$385
C)$424
D)$8,514
E)$1,537

Question 67

The present value of an ordinary annuity of $2,350 each year for 8 years, assuming an opportunity cost of 11 percent, is: (Round to the nearest whole dollar.)

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

Question 68

You are offered an investment that will pay you the cash flows shown in the table. The first cash flow occurs in one year. The cost of the investment is $1,086.59 (today). What is the return on the investment? $$\begin{array} { | c | c | } \hline \text { Year } & \text { Cash Flow } \\\hline 1 & \$ 70 \\\hline 2 & \$ 70 \\\hline 3 & \$ 70 \\\hline 4 & \$ 70 \\\hline 5 & \$ 1,070 \\\hline\end{array}$$

A)5%
B)7%
C)9%
D)11%
E)13%

Question 69

How much must be invested today to make four annual withdrawals of $20,000 each for tuition payments if you can earn 8% compounded annually on your investment and the first withdrawal will take place in one year? (Round to the nearest whole dollar)

A)$66,243
B)$51,242
C)$79,854
D)$47,393
E)$57,341

Question 70

The rate of return earned on an investment of $50,000 today that guarantees an annuity of $10,489 for six years in approximately:

A)5 percent
B)7 percent
C)30 percent
D)10 percent
E)12 percent

Question 71

What is the rate of return on an investment of $16,278 if the company expects to receive $3,000 per year for the next ten years?

A)18 percent
B)13 percent
C)8 percent
D)3 percent
E)10 percent

Question 72

Donna makes annual end of year payments of $5,403.71 on a four year loan with an interest rate of 13 percent. The original principal amount was: (Round to the nearest whole dollar)

A)$16,073
B)$22,139
C)$15,092
D)$17,175

Question 73

Mary will receive $12,000 per year for the next ten 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? (Round to the nearest whole dollar)

A)$120,114
B)$67,803
C)$65,640
D)$56,793

Question 74

The present value of an ordinary annuity of $350 each year for five years, assuming an opportunity cost of 4 percent, is: (Round to the nearest whole dollar)

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

Question 75

You are late paying a bill for $11,200.66. You have made arrangements to pay off the bill in installments of $260 per month, and you will be charged monthly interest of 1.2% on the balance owing. How long will it take you to pay off the account balance? (round your answer to nearest month)

A)61 months
B)60 months
C)62 months
D)63 months
E)64 months

Question 76

Find the present value of a 5-year annuity due if the annual payments are $600 and the interest rate is 11%. How much larger is the present value of the annuity due than the present value of the ordinary 5-year annuity?

A)$243.93
B)$204.76
C)$279.22
D)$261.32
E)$227.45

Question 77

You expect to receive $800 at the end of each of the next twenty years. What is the present value of the stream of payments if the interest rate is 6%?

A)$9,175.94
B)$9,411.26
C)$9,305.38
D)$9,687.79
E)$9,550.30

Question 78

You plan to retire at age 65. You want to withdraw $100,000 from your savings account every year starting on your 65 ^th birthday. You expect to make your final withdrawal on your 84^th birthday. How much must you have accumulated by your 65 ^th birthday in order to support your desired withdrawals if you earn 3% on your savings?

A)$1,532,379.91
B)$1,587,747.49
C)$1,475,351.31
D)$1,432,379.91
E)$1,090,095.56

Question 79

You have just take out a 30-year, $120,000 mortgage on your new home. This mortgage is to be repaid in 360 equal end-of-month installments. If each of the monthly installments is $1,500, what is the effective annual interest rate on this mortgage?

A)15.87%
B)14.75%
C)13.38%
D)16.25%
E)16.49%

Question 80

You are faced with two different investment options. The first investment provides cash flows of $1,500 per year for 10 years. The second investment provides cash flows of $3,000 for 5 years. For both investments, cash flows occur at the end of each year. Which of these has the higher present value with a discount rate of 5%?

A)The 5-year investment
B)They have the same PV.
C)The 10-year investment