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Starting to invest early for retirement increases the benefits of compound interest.

A) True
B) False

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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 B)
G) D) and E)

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

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Suppose you borrowed $14,000 at a rate of 10.0% and must repay it in 5 equal installments at the end of each of the next 5 years. How much interest would you have to pay in the first year?


A) $1,200.33
B) $1,263.50
C) $1,330.00
D) $1,400.00
E) $1,470.00

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

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Ten years ago, Lucas Inc. earned $0.50 per share. Its earnings this year were $2.20. What was the growth rate in earnings per share (EPS) over the 10-year period?


A) 15.17%
B) 15.97%
C) 16.77%
D) 17.61%
E) 18.49%

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

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Suppose you just won the state lottery, and you have a choice between receiving $2,550,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes.


A) 7.12%
B) 7.49%
C) 7.87%
D) 8.26%
E) 8.67%

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

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Suppose Sally Smith plans to invest $1,000. She can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be more than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)

A) True
B) False

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Suppose Randy Jones plans to invest $1,000. He can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be somewhat less than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)

A) True
B) False

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You sold a car and accepted a note with the following cash flow stream as your payment. What was the effective price you received for the car assuming an interest rate of 6.0%? You sold a car and accepted a note with the following cash flow stream as your payment. What was the effective price you received for the car assuming an interest rate of 6.0%? A) $5,987 B) $6,286 C) $6,600 D) $6,930 E) $7,277


A) $5,987
B) $6,286
C) $6,600
D) $6,930
E) $7,277

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

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At a rate of 6.5%, what is the future value of the following cash flow stream?


A) $526.01
B) $553.69
C) $582.83
D) $613.51
E) $645.80

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

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Your bank offers to lend you $100,000 at an 8.5% annual interest rate to start your new business. The terms require you to amortize the loan with 10 equal end-of-year payments. How much interest would you be paying in Year 2?


A) $7,531
B) $7,927
C) $8,323
D) $8,740
E) $9,177

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

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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) B) and D)

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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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Suppose a U.S. treasury bond will pay $2,500 five years from now. If the going interest rate on 5-year treasury bonds is 4.25%, how much is the bond worth today?


A) $1,928.78
B) $2,030.30
C) $2,131.81
D) $2,238.40
E) $2,350.32

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

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Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT?


A) The monthly payments will decline over time.
B) A smaller proportion of the last monthly payment will be interest, and a larger proportion will be principal, than for the first monthly payment.
C) The total dollar amount of principal being paid off each month gets smaller as the loan approaches maturity.
D) The amount representing interest in the first payment would be higher if the nominal interest rate were 7% rather than 10%.
E) Exactly 10% of the first monthly payment represents interest.

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

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What's the present value of $1,525 discounted back 5 years if the appropriate interest rate is 6%, compounded monthly?


A) $ 969
B) $1,020
C) $1,074
D) $1,131
E) $1,187

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

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Your aunt has $500,000 invested at 5.5%, and she now wants to retire. She wants to withdraw $45,000 at the beginning of each year, beginning immediately. She also wants to have $50,000 left to give you when she ceases to withdraw funds from the account. For how many years can she make the $45,000 withdrawals and still have $50,000 left in the end?


A) 15.54
B) 16.36
C) 17.22
D) 18.08
E) 18.99

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

Correct Answer

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Which of the following statements is CORRECT?


A) The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.
B) If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity.
C) The cash flows for an annuity due must all occur at the ends of the periods.
D) The cash flows for an annuity must all be equal, and they must occur at regular intervals, such as once a year or once a month.
E) 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.

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

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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 start a new business, 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) None of the above
G) B) and D)

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