978-0134083285 Chapter 5 Part 2

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5) If the interest rate is positive, then the present value of an annuity due will be less than the present

value of an ordinary annuity.

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

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

6) Joe borrowed $10,000 at 10% per year and promised to pay it back in equal annual installments at the

end of each of the next 5 years. Joe‘s payment will be $2,100 [($10,000/5) + ($10,000 × 10%)].

Keywords: Time Value of Money, Amortization Schedule

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

7) John has to pay $1,000 per month for his mortgage for another 5 years, but he is considering paying the

mortgage off in one lump sum. John cannot calculate the present value of the payments using the annuity

formulas because his payments are monthly and not once per year.

Keywords: Present Value, Annuity

Learning Obj.: L.O. 5.2

AACSB: Reflective Thinking

8) The present value of a deferred annuity (e.g., an annuity that starts 10 years from today) can be

calculated in two steps: (1) calculate the future value of the annuity, and (2) calculate the present value of

the amount determined in step (1).

Keywords: Annuity

Learning Obj.: L.O. 5.2

AACSB: Reflective Thinking

9) The present value of an annuity increases as the discount rate increases.

Keywords: Present Value, Annuity, Discount Rate

Learning Obj.: L.O. 5.2

AACSB: Reflective Thinking

10) To evaluate or compare investment proposals, we must adjust the value of all cash flows to a common

date.

Keywords: Time Value of Money

Learning Obj.: L.O. 5.2

AACSB: Reflective Thinking

11) An example of an annuity is the interest received from bonds.

Keywords: Annuity

Learning Obj.: L.O. 5.2

AACSB: Reflective Thinking

12) Bill saves $3,000 per year in his IRA starting at age 25 and continuing to age 65, when he retires. The

amount Bill has in his IRA at age 65 can be characterized as the future value of an annuity.

Keywords: Future Value of an Annuity

Learning Obj.: L.O. 5.2

AACSB: Reflective Thinking

13) When repaying an amortized loan, the interest payments increase over time due to the compounding

process.

Keywords: Loan Amortization, Interest Payments

Learning Obj.: L.O. 5.2

AACSB: Reflective Thinking

14) The value of a bond investment, which provides fixed interest payments, will increase when

discounted at an 8% rate rather than at an 11% rate.

Keywords: Discount Rate, Present Value, Annuity

Learning Obj.: L.O. 5.2

AACSB: Reflective Thinking

15) The future value of a 10-year ordinary annuity is twice as much as the future value of an otherwise

identical 5-year annuity.

Keywords: Future Value, Annuity, Time Periods

Learning Obj.: L.O. 5.2

AACSB: Reflective Thinking

16) The future value of an annuity due is greater than the future value of an otherwise identical ordinary

annuity.

Keywords: Future Value, Annuity Due, Ordinary Annuity

Learning Obj.: L.O. 5.2

AACSB: Reflective Thinking

17) If the interest rate is positive, a six-year ordinary annuity of $500 per year must have a present value

over $3,000.

Keywords: Ordinary Annuity, Present Value

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

18) A compound annuity involves depositing or investing a single sum of money and allowing it to

compound for a certain number of years.

Keywords: Compound Annuity

Learning Obj.: L.O. 5.2

AACSB: Reflective Thinking

19) Two sisters each open IRAs in 2011 and plan to invest $3,000 per year for the next 30 years. Mary

makes her first deposit on January 1, 2011, and will make all future deposits on the first day of the year.

Jane makes her first deposit on December 31, 2011, and will continue to make her annual deposits on the

last day of each year. At the end of 30 years, the difference in the value of the IRAs (rounded to the

nearest dollar), assuming an interest rate of 7% per year, will be

A) $19,837.

B) $12,456.

C) $6,300.

D) $210.

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

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

20) You have the choice of two equally risk annuities, each paying $5,000 per year for 8 years. One is an

annuity due and the other is an ordinary annuity. If you are going to be receiving the annuity payments,

which annuity would you choose to maximize your wealth?

A) the annuity due

B) the ordinary annuity

C) Since we don’t know the interest rate, we can’t find the value of the annuities and hence we cannot tell

which one is better.

D) either one because they have the same present value

Keywords: Annuity Due, Ordinary Annuity, Present Value

Learning Obj.: L.O. 5.2

AACSB: Reflective Thinking

21) D’Anthony borrowed $50,000 today that he must repay in 15 annual end–of-year installments of

$5,000. What annual interest rate is D’Anthony paying on his loan?

A) 2.222%

B) 3.333%

C) 5.556%

D) 33.33%

Keywords: Loan Amortization, Interest Rate, Annuity

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

22) Assume you are to receive a 10-year annuity with annual payments of $1000. The first payment will

be received at the end of Year 1, and the last payment will be received at the end of Year 10. You will

invest each payment in an account that pays 9 percent compounded annually. Although the annuity

payments stop at the end of year 10, you will not withdraw any money from the account until 25 years

from today, and the account will continue to earn 9% for the entire 25-year period. What will be the value

in your account at the end of Year 25 (rounded to the nearest dollar)?

A) $48,359

B) $35,967

C) $48,000

D) $55,340

Keywords: Future Value, Annuity, Single Sum

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

23) You deposit $5,000 per year at the end of each of the next 25 years into an account that pays 8%

compounded annually. How much could you withdraw at the end of each of the 20 years following your

last deposit if all withdrawals are the same dollar amount? (The twenty-fifth and last deposit is made at

the beginning of the 20-year period. The first withdrawal is made at the end of the first year in the 20-year

period.)

A) $18,276

B) $27,832

C) $37,230

D) $43,289

Keywords: Annuity, Future Value, Present Value, Payment

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

24) You charged $1,000 on your credit card for Christmas presents. Your credit card company charges

you 26% annual interest, compounded monthly. If you make the minimum payments of $25 per month,

how long will it take (to the nearest month) to pay off your balance?

A) 94 months

B) 79 months

C) 54 months

D) 40 months

Keywords: Annuity, Loan Amortization, Time Value of Money

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

25) You decide to borrow $250,000 to build a new home. The bank charges an interest rate of 8%

compounded monthly. If you pay back the loan over 30 years, what will your monthly payments be

(rounded to the nearest dollar)?

A) $1,123

B) $1,237

C) $1,687

D) $1,834

Keywords: Loan Amortization, Payment

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

26) Your grandparents deposit $2,000 each year on your birthday, starting the day you are born, in an

account that pays 7% interest compounded annually. How much will you have in the account on your

21st birthday, just after your grandparents make their deposit?

A) $101,802

B) $98,016

C) $86,058

D) $79,640

Keywords: Annuity, Future Value

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

27) You can buy a $50 savings bond today for $25 and redeem the bond in 10 years for its full face value

of $50. You could also put your money in a money-market account that pays 7% interest per year. Which

option is better, assuming they are of equal risk?

A) The money-market account is better because it pays more interest.

B) The money-market account is better because it requires a smaller investment.

C) The savings bond is better because it earns a higher interest rate.

D) The money market and savings bond both earn 7% interest, so they are equal in value.

Keywords: Time Value of Money, Interest Rates

Learning Obj.: L.O. 5.2

AACSB: Reflective Thinking

28) A 65 year-old man is retiring and can take either $500,000 in cash or an ordinary annuity that

promises to pay him $50,000 per year for as long as he lives. Which of the following statements is MOST

correct?

A) Because of the time value of money, the man will always be better off taking the $500,000 up front.

B) The higher the interest rate, the more likely the man will prefer the $500,000 lump sum.

C) If the man expects to live more than 10 years, then he will prefer the annuity.

D) If the man is certain the company will not default on its future payments, he should select the $50,000

per year.

Keywords: Ordinary Annuity

Learning Obj.: L.O. 5.2

AACSB: Reflective Thinking

29) A financial advisor tells you that you can make your child a millionaire if you just start saving early.

You decide to put an equal amount each year into an investment account that earns 7.5% interest per

year, starting on the day your child is born. How much would you need to invest each year (rounded to

the nearest dollar) to accumulate a million for your child by the time he is 35 years old? (Your last deposit

will be made on his 34th birthday.)

A) $6,525

B) $7,910

C) $12,500

D) $20,347

Keywords: Annuity, Payments

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

30) You are 21 years old today. Your grandparents set up a trust fund that will pay you $25,000 per year

for 20 years, starting on your 65th birthday to supplement your retirement. If the trust can earn 7.5% per

year, how much will your grandparents need to put in the trust fund today (rounded to the nearest ten

dollars)?

A) $11,370

B) $22,310

C) $5,250

D) $17,450

Keywords: Annuity, Present Value

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

31) You estimate you‘ll need $200,000 per year for 25 years starting on your 65th birthday to live on

during your retirement. Today is your 50th birthday and you want to make equal deposits into an

account paying 9% interest per year, the first deposit today and the last deposit on your 64th birthday.

How much must each deposit be (rounded to the nearest $10)?

A) $99,920

B) $85,840

C) $66,909

D) $49,380

Keywords: Annuity, Present Value, Future Value

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

32) It is your 6th birthday today. You have a trust fund with $50,000 that is earning 8% per year. You

expect to withdraw $30,000 per year for 7 years starting on your 22nd birthday for graduate school. How

much money will be left in the trust fund after your last withdrawal (rounded to the nearest $10)?

A) $125,660

B) $35,780

C) $4,140

D) You will not have enough money to pay for graduate school.

Keywords: Annuity, Future Value, Single Sum

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

33) You own an annuity due contract that will pay you $3,000 per year for 12 years. You need money to

pay back a loan in 5 years, and you are afraid if you get the annuity payments annually you will spend

the money and not be able to pay back your loan. You decide to sell your annuity for a lump sum of cash

to be paid to you five years from today. If the interest rate is 8%, what is the equivalent value of your 12-

year annuity if paid in one lump sum five years from today?

A) $22,008

B) $18,000

C) $35,876

D) $38,880

Keywords: Ordinary Annuity, Future Value, Present Value

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

34) Your daughter is born today and you want her to be a millionaire by the time she is 35 years old. You

open an investment account that promises to pay 12% per year. How much money must you deposit each

year, starting on her 1st birthday and ending on her 35th birthday, so your daughter will have $1,000,000

by her 35th birthday?

A) $2,317

B) $3,455

C) $5,777

D) $9,450

Keywords: Annuity, Payments

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

35) You borrow $25,000 to be repaid in 12 monthly installments of $2,292.00. The annual interest rate is

closest to

A) 1.5 percent.

B) 12 percent.

C) 18 percent.

D) 24 percent.

Keywords: Loan Amortization, Interest Rate

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

36) You sell valuable artifacts from your household estate for $200,000 and want to use the money to

supplement your retirement. You receive the money on your 60th birthday, the day you retire. You want

to withdraw equal amounts at the end of each of the next 25 years. What constant amount can you

withdraw each year and have nothing remaining at the end of 20 years if you are earning 7% interest per

year?

A) $17,162

B) $28,318

C) $37,574

D) $49,113

Keywords: Annuity, Payments

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

37) You inherit $300,000 from your parents and want to use the money to supplement your retirement.

You receive the money on your 65th birthday, the day you retire. You want to withdraw equal amounts

at the end of each of the next 20 years. What constant amount can you withdraw each month and have

nothing remaining at the end of 20 years if you are earning 7% interest compounded monthly?

A) $1,200

B) $1,829

C) $2,326

D) $2,943

Keywords: Annuity, Payments

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

38) Auto Loans R Them loans you $24,000 for four years to buy a car. The loan must be repaid in 48 equal

monthly payments. The annual interest rate on the loan is 9 percent. What is the monthly payment?

A) $500.92

B) $543.79

C) $563.82

D) $597.24

Keywords: Loan Amortization, Payment, Monthly Compounding

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

39) Your company has received a $50,000 loan from an industrial finance company. The annual payments

are $6,202.70. If the company is paying 9 percent interest per year, how many loan payments must the

company make?

A) 15

B) 13

C) 12

D) 19

Keywords: Loan Amortization, Loan Payments

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

40) What is the present value of an annuity of $4,000 received at the beginning of each year for the next

eight years? The first payment will be received today, and the discount rate is 9% (round to nearest $1).

A) $36,288

B) $35,712

C) $25,699

D) $24,132

Keywords: Present Value, Annuity Due

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

41) What is the present value of an annuity of $120 received at the end of each year for 11 years? Assume

a discount rate of 7%. The first payment will be received one year from today (round to nearest $1).

A) $250

B) $400

C) $570

D) $900

Keywords: Present Value, Annuity

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking