978-0134083285 Chapter 5 Part 3

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42) A deferred annuity will pay you $500 at the end of each year for 10 years, however the first payment

will not be made until three years from today (payments will be made at the end of years 3 through 12).

What amount will you have to deposit today to fund this deferred annuity? Use an 8% discount rate and

round your answer to the nearest $100.

A) $2,200

B) $2,400

C) $2,900

D) $3,400

Keywords: Deferred Annuity, Present Value

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

43) Charlie wants to retire in 15 years, and he wants to have an annuity of $50,000 a year for 20 years after

retirement. Charlie wants to receive the first annuity payment the day he retires. Using an interest rate of

8%, how much must Charlie invest today in order to have his retirement annuity (rounded to nearest

$10)?

A) $167,130

B) $200,450

C) $256,890

D) $315,240

Keywords: Present Value, Annuity Due, Deferred Annuity

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

44) It is January 1st and Darwin Davis has just established an IRA (Individual Retirement Account).

Darwin will put $1000 into the account on December 31st of this year and at the end of each year for the

following 39 years (40 years total). How much money will Darwin have in his account at the end of the

40th year? Assume that the account pays 12% interest compounded annually and round to nearest $1000.

A) $93,000

B) $766,000

C) $767,000

D) $850,000

Keywords: Annuity, Future Value

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

45) If you put $10 in a savings account at the beginning of each month for 15 years, how much money will

be in the account at the end of the 10th year? Assume that the account earns 12% compounded monthly

and round to the nearest $1.

A) $1,200

B) $2,323

C) $5,046

D) $3,485

Keywords: Future Value, Annuity Due

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

46) If you put $200 in a savings account at the beginning of each year for 10 years and then allow the

account to compound for an additional 10 years, how much will be in the account at the end of the 20th

year? Assume that the account earns 10% and round to the nearest $100.

A) $8,300

B) $9,100

C) $8,900

D) $9,700

Keywords: Future Value, Annuity, Single Sum

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

47) How much money must you pay into an account at the end of each of 20 years in order to have

$100,000 at the end of the 20th year? Assume that the account pays 6% per year, and round to the nearest

$1.

A) $1,840

B) $2,028

C) $2,195

D) $2,718

Keywords: Annuity Due, Future Value, Annual Payment

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

48) How much money must you pay into an account at the beginning of each of 20 years in order to have

$10,000 at the end of the 20th year? Assume that the account pays 12% per year, and round to the nearest

$1.

A) $1,195

B) $111

C) $124

D) $139

Keywords: Annuity Due, Future Value, Annual Payment

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

49) You are going to pay $800 into an account at the beginning of each of 20 years. The account will then

be left to compound for an additional 20 years until the end of year 40, when it will turn into a perpetuity.

You will receive the first payment from the perpetuity at the end of the 41st year. If the account pays 14%,

how much will you receive from the perpetuity each year (rounded to nearest $1,000)?

A) $140,000

B) $150,000

C) $160,000

D) $170,000

Keywords: Annuity Due, Future Value, Perpetuity

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

50) You are going to pay $100 into an account at the beginning of each of the next 40 years. At the

beginning of the 41st year you buy a 30 year annuity whose first payment comes at the end of the 41st

year (the accounts earn 12%). How much will you receive at the end of the 41st year (i.e., the first annuity

payment). Round to nearest $100.

A) $93,000

B) $7,800

C) $11,400

D) $10,700

Keywords: Annuity Due, Ordinary Annuity, Future Value, Present Value, Annual Payment

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

51) A retirement plan guarantees to pay you or your estate a fixed amount for 25 years. At the time of

retirement you will have $100,000 to your credit in the plan. The plan anticipates earning 7% interest

annually over the period you receive benefits. How much will your annual benefits be assuming the first

payment occurs one year from your retirement date?

A) $6,182

B) $7,272

C) $8,101

D) $8,581

Keywords: Annuity, Annual Payment, Present Value

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

52) You have been accepted to study international economy at the European Central Bank (ECB) in

Frankfurt. You will need $10,500 every 6 months (beginning today) for the next three years to cover

tuition and living expenses. Mom and Dad have agreed to pay for your education, and want to make one

deposit today in a bank account earning 6% interest, compounded semiannually. How much must they

deposit now so that you can withdraw $10,500 at the beginning of each semester over the next 3 years?

A) $54,187

B) $55,797

C) $58,587

D) $56,639

Keywords: Annuity Due, Present Value

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

53) You are thinking of buying a craft emporium. It is expected to generate cash flows of $30,000 per year

in years 1 through 5, and $40,000 per year in years 6 through 10. If the appropriate discount rate is 8%,

what amount are you willing to pay for the emporium?

A) $135,288

B) $167,943

C) $215,048

D) $228,476

Keywords: Present Value, Annuity Due, Deferred Annuity

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

54) You have contracted to buy a house for $250,000, paying $30,000 down and taking out a fully

amortizing loan for the balance, at a 5.7% annual rate for 30 years. What will your monthly payment be if

they make equal monthly installments over the next 30 years (to the nearest dollar)?

A) $1,035

B) $1,123

C) $1,189

D) $1,277

Keywords: Loan Amortization, Monthly Payments

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

55) You bought a racehorse that has had a winning streak for six years, bringing in $250,000 at the end of

each year before dying of a heart attack. If you paid $1,155,720 for the horse 4 years ago, what was your

annual return over this 4-year period?

A) 8%

B) 33%

C) 18%

D) 12%

Keywords: Annuity, Future Value, Rate of Return

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

56) Jimmy just bought a new Ford SUV for his business. The price of the vehicle was $40,000. Jimmy

made a $5,000 down payment and took out an amortized loan for the rest. The car dealership made the

loan at 8% interest compounded monthly for five years. He is to pay back the principal and interest in

equal monthly installments beginning one month from now. Determine the amount of Jimmy’s monthly

payment.

A) $634.56

B) $709.67

C) $745.87

D) $809.33

Keywords: Loan Amortization, Monthly Payment, Annuity

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

57) You just graduated and landed your first job in your new career. You remember that your favorite

finance professor told you to begin the painless job of saving for retirement as soon as possible, so you

decided to put away $2,000 at the end of each year in a Roth IRA. Your expected annual rate of return on

the IRA is 7.5%. How much will you accumulate at retirement after 40 years of investing? (Note: this may

assume that you are even retiring early.)

A) $94,426

B) $247,921

C) $1,088,632

D) $454,513

Keywords: Annuity, Future Value, IRA

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

58) Congratulations! You are the proud winner of the multi-state Sour Ball Lottery. You are to receive

$2,000,000 at the end of each year for the next 20 years. While the Lottery Commission refers to this as a

$40,000,000 jackpot, if you choose the “cash option” they will give you much less than that; you can

receive a lump sum payment today equal to the present value of the ordinary annuity instead of the 20

annual payments. If the discount rate that the Lottery Commission uses to determine the lump sum

payoff is 7%, what is your payoff if you select the cash option?

A) $26,945,332

B) $39,707,503

C) $42,977,401

D) $21,188,028

Keywords: Annuity, Present Value

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

59) You are ready to retire. A glance at your 401(k) statement indicates that you have $750,000. If the

funds remain in an account earning 9.0%, how much could you withdraw at the beginning of each year

for the next 25 years?

A) $55,620

B) $70,050

C) $35,830

D) $2,500

Keywords: Annuity Due, Annual Payment

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

60) How much would you be willing to pay (rounded to the nearest dollar) for a 20-year annuity due if

the payments are $4,500 per year and you want to earn a rate of return equal to 5.5% per year?

A) $84,500

B) $63,445

C) $56,734

D) $53,777

Keywords: Annuity Due, Present Value

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

61) How much would you be willing to pay (rounded to the nearest dollar) for a 20-year ordinary annuity

if the payments are $4,500 per year and you want to earn a rate of return equal to 5.5% per year?

A) $84,500

B) $63,445

C) $56,734

D) $53,777

Keywords: Ordinary Annuity, Present Value

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

62) Manny and Irene will be retiring in fifteen years and would like to buy a Mexican villa. The villa costs

$500,000 today, and housing prices in Mexico are expected to increase by 6% per year. Manny and Irene

want to make fifteen equal annual payments into an account, starting today, so there will be enough

money to purchase the villa in fifteen years. If the account earns 10% per year, what is the amount of each

deposit?

A) $79,885

B) $72,623

C) $34,286

D) $32,947

Keywords: Future Value, Annuity Payments, Annuity Due

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

63) Your daughter is born today and you want her to be a millionaire by the time she is 40 years old. open

an investment account that promises to pay 11.5% per year. How much money must you deposit today so

your daughter will have $1,000,000 by her 35th birthday?

A) $28,575

B) $22,150

C) $20,100

D) $18,940

Keywords: Present Value

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

64) Your son is born today and you want to make him a millionaire by the time he is 50 years old. You

deposit $10,700 in an investment account and want to know what annual interest rate must you earn in

order to have the account value equal to $1,000,000 on your son’s 50th birthday.

A) 17.8%

B) 12.4%

C) 9.5%

D) 6.2%

Keywords: Compound Interest, Time Value of Money

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

65) A bond matures in 20 years, at which time it pays the owner $1,000. It also pays $70 at the end of each

of the next 20 years. If similar bonds are currently yielding 7%, what is the market value of the bond?

A) over $1,000

B) under $1,000

C) exactly $1,000

D) cannot be determined from the information given

Keywords: Present Value, Bond

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

66) Your son will be attending an expensive university in 12 years. You deposit $5,000 per year for 12

years, beginning today. How much money will be in the college fund 12 years from now if the fund earns

8% per year?

Keywords: Future Value, Annuity Due

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

67) If you wish to accumulate $200,000 in the child’s college fund after 18 years, and can invest at a 7.5%

annual rate, how much must you invest at the end of each year if the first deposit is made at the end of

the first year?

Keywords: Annuity, Annual Payment

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

68) Betty borrows $60,000 at 12 percent compounded annually. The loan is to be repaid in five equal

annual end-of-year installments. How much must each loan payment be?

Keywords: Present Value, Annuity, Loan Amortization

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

69) You are currently 25 years of age. You have developed a lifetime budget that includes $50,000 at age

40 for a college fund for your kids and $25,000 per year for 20 years to supplement your retirement, the

first payment on your 60th birthday and the last payment on your 79th birthday. You open an investment

account on your 25th birthday that promises to pay 9% interest compounded annually. You want to

deposit equal annual amounts into the account every year on your birthday, starting today (your 25th

birthday) and continuing until you are 40 years old (i.e., the last deposit is made on your 40th birthday).

How much will each deposit have to be if you want to meet your financial goals?

Keywords: Time Value of Money, Annuity, Present Value

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

70) Bob invested $2,000 in an investment fund on his 21st birthday. The fund pays 7% interest

compounded semiannually. Bob is celebrating his 50th birthday today. Bob decides he wants to retire on

his 60th birthday and he wants to withdraw $75,000 per year, the first withdrawal on his 60th birthday

and the last withdrawal on his 90th birthday. Bob expects to receive $100,000 from his employer on his

55th birthday in recognition of his long service to the company. Assume Bob has not taken any money

out of his investment fund since he initially funded it on his 21st birthday, and that he will deposit the

$100,000 from his employer into the investment fund on his 55th birthday. The investment fund will be

used to pay for Bob’s retirement.

If Bob makes no additional deposits into his investment fund, how much will be available for retirement

at age 60?

Since the amount in (a) is insufficient to meet his retirement goals, Bob decides to deposit equal annual

amounts into the investment fund beginning on his 51st birthday and ending on his 59th birthday, so that

he can meet his retirement goals. How much will each deposit be?

Keywords: Annuity Due, Annuity, Time Value of Money, Future Value, Present Value

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

71) Bill starts a retirement fund at age 21 and plans on depositing equal annual amounts on each

birthday, starting at age 21, and ending at age 60. He wants to have $2 million at age 60. John starts his

fund on his 30th birthday. He wants to deposit equal annual amounts on each birthday starting on his

30th birthday and ending on his 60th birthday. John wants to have $2 million at age 60. If the investment

funds earn 10% per year, calculate the amounts the Bill and John respectively will have to save each year

(rounded to the nearest dollar) to meet their goals. Comment on the difference.

Keywords: Annuity Due, Annuity, Time Value of Money, Future Value, Present Value

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

72) An investment promises to pay you the following amounts at the end of each of the next 10 years: (1)

$1,000, (2) $2,000, (3) $3,000, (4) $4,000, (5) – (10) $5,000 per year. If you want to earn a return of 8% per

year, how much will you be willing to pay for the investment today?

Keywords: Deferred Annuity, Present Value, Uneven Cash Flows

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking