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You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?


A) 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.
B) 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.
C) The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE.
D) The present value of DUE exceeds the present value of ORD, and the future value of DUE also exceeds the future value of ORD.
E) 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.

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

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Time lines cannot be constructed for annuities unless all the payments occur at the end of the periods.

A) True
B) False

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Your uncle is about to retire, and he wants to buy an annuity that will provide him 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 him to buy the annuity today?


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

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

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

A) True
B) False

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What is the present value of the following cash flow stream at a rate of 8.0%?


A) $7,917
B) $8,333
C) $8,772
D) $9,233
E) $9,695

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

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Which of the following statements is CORRECT?


A) A time line is not meaningful unless all cash flows occur annually.
B) Time lines are not useful for visualizing complex problems prior to doing actual calculations.
C) Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly.
D) Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.
E) Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven amounts.

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

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You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would increase the calculated value of the investment?


A) The cash flows are in the form of a deferred annuity, and they total to $100,000. You learn that the annuity lasts for 10 years rather than 5 years, hence that each payment is for $10,000 rather than for $20,000.
B) The discount rate decreases.
C) The riskiness of the investment's cash flows increases.
D) The total amount of cash flows remains the same, but more of the cash flows are received in the later years and less are received in the earlier years.
E) The discount rate increases.

F) C) and E)
G) A) and C)

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You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning?


A) 7.62%
B) 8.00%
C) 8.40%
D) 8.82%
E) 9.26%

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

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What's the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%?


A) $4,750
B) $5,000
C) $5,250
D) $5,513
E) $5,788

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

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Then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. They expect their investment account to earn 9%. How large must the annual payments at t = 5, 6, and 7 be to cover Ellen's anticipated college costs?


A) $1,965.21
B) $2,068.64
C) $2,177.51
D) $2,292.12
E) $2,412.76

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

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Last year Thomson Inc's earnings per share were $3.50, and its growth rate during the prior 5 years was 9.0% per year. If that growth rate were maintained, how many years would it take for Thomson's EPS to triple?


A) 9.29
B) 10.33
C) 11.47
D) 12.75
E) 14.02

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

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Your father's employer was just acquired, and he was given a severance payment of $375,000, which he invested at a 7.5% annual rate. He now plans to retire, and he wants to withdraw $35,000 at the end of each year, starting at the end of this year. How many years will it take to exhaust his funds, i.e., run the account down to zero?


A) 22.50
B) 23.63
C) 24.81
D) 26.05
E) 27.35

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

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Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant?


A) The present value of a 5-year, $250 annuity due will be lower than the PV of a similar ordinary annuity.
B) A 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year mortgage.
C) A bank loan's nominal interest rate will always be equal to or less than its effective annual rate.
D) If an investment pays 10% interest, compounded annually, its effective annual rate will be less than 10%.
E) Banks A and B offer the same nominal annual rate of interest, but A pays interest quarterly and B pays semiannually. Deposits in Bank B will provide the higher future value if you leave your funds on deposit.

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

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Suppose you have $1,500 and plan to purchase a 5-year certificate of deposit (CD) that pays 3.5% interest, compounded annually. How much will you have when the CD matures?


A) $1,781.53
B) $1,870.61
C) $1,964.14
D) $2,062.34
E) $2,165.46

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

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You plan to invest in bonds that pay 6.0%, compounded annually. If you invest $10,000 today, how many years will it take for your investment to grow to $30,000?


A) 12.37
B) 13.74
C) 15.27
D) 16.97
E) 18.85

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

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Your child's orthodontist offers you two alternative payment plans. The first plan requires a $4,000 immediate up-front payment. The second plan requires you to make monthly payments of $137.41, payable at the end of each month for 3 years. What nominal annual interest rate is built into the monthly payment plan?


A) 12.31%
B) 12.96%
C) 13.64%
D) 14.36%
E) 15.08%

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

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What's the present value of $4,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually?


A) $3,089
B) $3,251
C) $3,422
D) $3,602
E) $3,782

F) B) and D)
G) A) and B)

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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) $16,035.87
C) $16,837.67
D) $17,679.55
E) $18,563.53

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

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What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 5.5%?


A) $16,576
B) $17,449
C) $18,367
D) $19,334
E) $20,352

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

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Suppose you inherited $275,000 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) B) and E)
G) A) and D)

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