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As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or less than the nominal rate on the deposit (or loan).

A) True
B) False

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Your aunt wants to retire and has $375,000.She expects to live for another 25 years, and she also expects to earn 7.5% on her invested funds.How much could she withdraw at the beginning of each of the next 25 years and end up with zero in the account?


A) $28,243.21
B) $29,729.70
C) $31,294.42
D) $32,859.14
E) $34,502.10

F) C) and D)
G) B) and E)

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Which of the following statements regarding a 15-year (180-month) $225,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)


A) The outstanding balance declines at a faster rate in the later years of the loan's life.
B) The remaining balance after three years will be $125,000 less one third of the interest paid during the first three years.
C) Because the outstanding balance declines over time, the monthly payments will also decline over time.
D) Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant.
E) The proportion of the monthly payment that goes towards repayment of principal will be lower 10 years from now than it will be the first year.

F) A) and D)
G) A) and E)

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You are considering investing in a European bank account that pays a nominal annual rate of 18%, compounded monthly.If you invest $5,000 at the beginning of each month, how many months would it take for your account to grow to $250,000? Round fractional months up.


A) 23
B) 27
C) 32
D) 38
E) 44

F) B) and D)
G) B) and E)

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Wildwoods, Inc.earned $1.50 per share five years ago.Its earnings this year were $3.20.What was the growth rate in earnings per share (EPS) over the 5-year period?


A) 15.54%
B) 16.36%
C) 17.18%
D) 18.04%
E) 18.94%

F) D) and E)
G) A) and D)

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Suppose you earned a $275,000 bonus this year and invested it at 8.25% per year.How much could you withdraw at the end of each of the next 20 years?


A) $28,532
B) $29,959
C) $31,457
D) $33,030
E) $34,681

F) A) and B)
G) B) and E)

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Which of the following statements is CORRECT?


A) If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity.
B) The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.
C) If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity.
D) The cash flows for an annuity due must all occur at the beginning of the periods.
E) The cash flows for an annuity may vary from period to period, but they must occur at regular intervals, such as once a year or once a month.

F) A) and D)
G) A) and C)

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Because your mother is about to retire, she wants to buy an annuity that will provide her with $75,000 of income a year for 20 years, with the first payment coming immediately.The going rate on such annuities is 5.25%.How much would it cost her to buy the annuity today?


A) $825,835
B) $869,300
C) $915,052
D) $963,213
E) $1,011,374

F) D) and E)
G) B) and D)

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Your friend offers to pay you an annuity of $2,500 at the end of each year for 3 years in return for cash today.You could earn 5.5% on your money in other investments with equal risk.What is the most you should pay for the annuity?


A) $5,493.71
B) $5,782.85
C) $6,087.21
D) $6,407.59
E) $6,744.83

F) A) and D)
G) C) and D)

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You plan to work for Strickland Corporation for 12 years after graduation and after that want to start your own business.You expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t = 6) and $15,000 annually for the following 6 years (t = 7 through t = 12) .The first deposit will be made a year from today.In addition, your grandmother just gave you a $25,000 graduation gift that you will deposit immediately (t = 0) .If the account earns 9% compounded annually, how much will you have when you start your business 12 years from now?


A) $238,176
B) $250,712
C) $263,907
D) $277,797
E) $291,687

F) None of the above
G) D) and E)

Correct Answer

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Assume that you own an annuity that will pay you $15,000 per year for 12 years, with the first payment being made today.You need money today to open a new restaurant, and your uncle offers to give you $120,000 for the annuity.If you sell it, what rate of return would your uncle earn on his investment?


A) 6.85%
B) 7.21%
C) 7.59%
D) 7.99%
E) 8.41%

F) All of the above
G) A) and E)

Correct Answer

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A time line is not meaningful unless all cash flows occur annually.

A) True
B) False

Correct Answer

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How much would $20,000 due in 50 years be worth today if the discount rate were 7.5%?


A) $438.03
B) $461.08
C) $485.35
D) $510.89
E) $537.78

F) A) and D)
G) A) and C)

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Cyberhost Corporation's sales were $225 million last year.If sales grow at 6% per year, how large (in millions) will they be 5 years later?


A) $271.74
B) $286.05
C) $301.10
D) $316.16
E) $331.96

F) A) and D)
G) C) and D)

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Your bank offers a savings account that pays 3.5% interest, compounded annually.How much will $500 invested today be worth at the end of 25 years?


A) $1,122.54
B) $1,181.62
C) $1,240.70
D) $1,302.74
E) $1,367.88

F) A) and B)
G) A) and C)

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If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by dividing the periodic rate by the number of periods per year.

A) True
B) False

Correct Answer

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A $150,000 loan is to be amortized over 6 years, with annual end-of-year payments.Which of these statements is CORRECT?


A) The proportion of interest versus principal repayment would be the same for each of the 7 payments.
B) The annual payments would be larger if the interest rate were lower.
C) If the loan were amortized over 10 years rather than 6 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 6-year amortization plan.
D) The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were lower.
E) The proportion of each payment that represents interest versus repayment of principal would be higher if the interest rate were higher.

F) A) and B)
G) A) and C)

Correct Answer

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You are considering two equally risky annuities, each of which pays $15,000 per year for 20 years.Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due.Which of the following statements is CORRECT?


A) If the going rate of interest decreases from 10% to 0%, the difference between the present value of ORD and the present value of DUE would remain constant.
B) The present value of ORD must exceed the present value of DUE, but the future value of ORD may be less than the future value of DUE.
C) The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD.
D) The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE.
E) The present value of DUE exceeds the present value of ORD, and the future value of DUE also exceeds the future value of ORD.

F) C) and E)
G) None of the above

Correct Answer

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You just deposited $2,500 in a bank account that pays a 4.0% nominal interest rate, compounded quarterly.If you also add another $5,000 to the account one year (4 quarters) from now and another $7,500 to the account two years (8 quarters) from now, how much will be in the account three years (12 quarters) from now?


A) $15,234.08
B) $16,035.88
C) $16,837.67
D) $17,679.55
E) $18,563.53

F) All of the above
G) B) and D)

Correct Answer

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Which of the following statements is CORRECT?


A) An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%.
B) The present value of a 3-year, $150 ordinary annuity will exceed the present value of a 3-year, $150 annuity due.
C) If a loan has a nominal annual rate of 7%, then the effective rate will never be less than 7%.
D) If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different.
E) The proportion of the payment that goes toward interest on a fully amortized loan increases over time.

F) D) and E)
G) C) and E)

Correct Answer

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