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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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You have a chance to buy an annuity that pays $2,500 at the end of each year for 3 years. 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)

Correct Answer

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Pacific 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) C) and D)
G) A) and B)

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Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.

A) True
B) False

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You borrowed $50,000 which you must repay in 10 years. You plan to make an initial deposit today, then make 9 more deposits at the beginning of each the next 9 years, but with the deposits increasing at the inflation rate. You expect to earn 5% on your funds, and you expect a 3% inflation rate. To the nearest dollar, how large must your initial deposit be to enable you to reach your $50,000 target?


A) $3,008
B) $3,342
C) $3,676
D) $4,044
E) $4,448

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

Correct Answer

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

Correct Answer

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Which of the following investments would have the highest future value at the end of 10 years? Assume that the effective annual rate for all investments is the same and is greater than zero.


A) Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments) .
B) Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments) .
C) Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments) .
D) Investment D pays $2,500 at the end of 10 years (just one payment) .
E) Investment E pays $250 at the end of every year for the next 10 years (a total of 10 payments) .

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

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Suppose your credit card issuer states that it charges a 15.00% nominal annual rate, but you must make monthly payments, which amounts to monthly compounding. What is the effective annual rate?


A) 15.27%
B) 16.08%
C) 16.88%
D) 17.72%
E) 18.61%

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

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Last year Tempe Corporation's sales were $525 million. If sales grow at 7.5% per year, how large (in millions) will they be 8 years later?


A) $845.03
B) $889.51
C) $936.33
D) $983.14
E) $1,032.30

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

Correct Answer

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All other things held constant, the present value of a given annual annuity decreases as the number of periods per year increases.

A) True
B) False

Correct Answer

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

A) True
B) False

Correct Answer

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Which of the following investments would have the lowest present value? Assume that the effective annual rate for all investments is the same and is greater than zero.


A) Investment A pays $250 at the end of every year for the next 10 years (a total of 10 payments) .
B) Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments) .
C) Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments) .
D) Investment D pays $2,500 at the end of 10 years (just one payment) .
E) Investment E pays $250 at the beginning of every year for the next 10 years (a total of 10 payments) .

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

Correct Answer

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

Correct Answer

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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 greater than its effective annual rate.
D) If an investment pays 10% interest, compounded quarterly, its effective annual rate will be greater 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) A) and C)
G) None of the above

Correct Answer

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

A) True
B) False

Correct Answer

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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

Correct Answer

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Suppose the U.S. Treasury offers to sell you a bond for $3,000. No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $5,000. What interest rate would you earn if you bought this bond at the offer price?


A) 3.82%
B) 4.25%
C) 4.72%
D) 5.24%
E) 5.77%

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

Correct Answer

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Time lines can be constructed in situations where some of the cash flows occur annually but others occur quarterly.

A) True
B) False

Correct Answer

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Which of the following statements regarding a 15-year (180-month) $125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)


A) The remaining balance after three years will be $125,000 less one third of the interest paid during the first three years.
B) Because it is a fixed-rate mortgage, the monthly loan payments (which include both interest and principal payments) are constant.
C) Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant.
D) 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.
E) The outstanding balance declines at a slower rate in the later years of the loan's life.

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

Correct Answer

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