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What's the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,000 at the end of Year 4 if the interest rate is 5%?


A) $ 8,509
B) $ 8,957
C) $ 9,428
D) $ 9,924
E) $10,446

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

Correct Answer

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Midway through the life of an amortized loan, the percentage of the payment that represents interest could be equal to, less than, or greater than to the percentage that represents repayment of principal. The proportions depend on the original life of the loan and the interest rate.

A) True
B) False

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Your father is about to retire, and he wants to buy an annuity that will provide him with $85,000 of income a year for 25 years, with the first payment coming immediately. The going rate on such annuities is 5.15%. How much would it cost him to buy the annuity today?


A) $1,063,968
B) $1,119,966
C) $1,178,912
D) $1,240,960
E) $1,303,008

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

Correct Answer

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Disregarding risk, if money has time value, it is impossible for the future value of a given sum to exceed its present value.

A) True
B) False

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Sue now has $125. How much would she have after 8 years if she leaves it invested at 8.5% with annual compounding?


A) $205.83
B) $216.67
C) $228.07
D) $240.08
E) $252.08

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

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Which of the following statements is CORRECT?


A) The present value of a 3-year, $150 annuity due will exceed the present value of a 3-year, $150 ordinary annuity.
B) If a loan has a nominal annual rate of 8%, then the effective rate can never be greater than 8%.
C) If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different.
D) The proportion of the payment that goes toward interest on a fully amortized loan increases over time.
E) An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%.

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

Correct Answer

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You just inherited some money, and a broker offers to sell you an annuity that pays $5,000 at the end of each year for 20 years. You could earn 5% on your money in other investments with equal risk. What is the most you should pay for the annuity?


A) $50,753
B) $53,424
C) $56,236
D) $59,195
E) $62,311

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

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Charter Bank pays a 4.50% nominal rate on deposits, with monthly compounding. What effective annual rate (EFF%) does the bank pay?


A) 3.72%
B) 4.13%
C) 4.59%
D) 5.05%
E) 5.56%

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

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Your sister turned 35 today, and she is planning to save $7,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that's expected to provide a return of 7.5% per year. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend each year after she retires? Her first withdrawal will be made at the end of her first retirement year.


A) $58,601
B) $61,686
C) $64,932
D) $68,179
E) $71,588

F) A) and B)
G) None of the above

Correct Answer

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

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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 lower 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 only 5 rather than 10 years, hence that each payment is for $20,000 rather than for $10,000.
B) The discount rate increases.
C) The riskiness of the investment's cash flows decreases.
D) The total amount of cash flows remains the same, but more of the cash flows are received in the earlier years and less are received in the later years.
E) The discount rate decreases.

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

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

A) True
B) False

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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) C) and E)
G) All of the above

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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 can be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly.
D) Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities.
E) Time lines cannot be constructed where some of the payments constitute an annuity but others are unequal and thus are not part of the annuity.

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

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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

Correct Answer

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Suppose an Exxon Corporation bond will pay $4,500 ten years from now. If the going interest rate on safe 10-year bonds is 4.25%, how much is the bond worth today?


A) $2,819.52
B) $2,967.92
C) $3,116.31
D) $3,272.13
E) $3,435.74

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

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Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?


A) The periodic rate of interest is 1.5% and the effective rate of interest is 3%.
B) The periodic rate of interest is 6% and the effective rate of interest is greater than 6%.
C) The periodic rate of interest is 1.5% and the effective rate of interest is greater than 6%.
D) The periodic rate of interest is 3% and the effective rate of interest is 6%.
E) The periodic rate of interest is 6% and the effective rate of interest is also 6%.

F) None of the above
G) A) and B)

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A time line is meaningful even if all cash flows do not occur annually.

A) True
B) False

Correct Answer

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Your subscription to Investing Wisely Weekly is about to expire. You plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for $850, also payable immediately. Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy?


A) 7.48
B) 8.80
C) 10.35
D) 12.18
E) 14.33

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

Correct Answer

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

Correct Answer

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