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If the discount (or interest) rate is positive, the present value of an expected series of payments will always exceed the future value of the same series.

A) True
B) False

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The present value of a future sum decreases as either the discount rate or the number of periods per year increases, other things held constant.

A) True
B) False

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

Correct Answer

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

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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) 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 greater than the nominal rate on the deposit (or loan).

A) True
B) False

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

A) True
B) False

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You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly. If you invest $3,000 at the end of each month, how many months will it take for your account to grow to $150,000?


A) 39.60
B) 44.00
C) 48.40
D) 53.24
E) 58.57

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

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You are negotiating to make a 7-year loan of $25,000 to Breck Inc. To repay you, Breck will pay $2,500 at the end of Year 1, $5,000 at the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently unspecified cash flow, X, at the end of each year from Year 4 through Year 7. Breck is essentially riskless, so you are confident the payments will be made. You regard 8% as an appropriate rate of return on a low risk but illiquid 7-year loan. What cash flow must the investment provide at the end of each of the final 4 years, that is, what is X?


A) $4,271.67
B) $4,496.49
C) $4,733.15
D) $4,969.81
E) $5,218.30

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

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Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years. How large would your payments be?


A) $3,704.02
B) $3,889.23
C) $4,083.69
D) $4,287.87
E) $4,502.26

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

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The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the smaller the percentage of the payment that will be a repayment of principal.

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

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

Correct Answer

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Some of the cash flows shown on a time line can be in the form of annuity payments but none can be uneven amounts.

A) True
B) False

Correct Answer

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Your girlfriend just won the Florida lottery. She has the choice of $15,000,000 today or a 20-year annuity of $1,050,000, with the first payment coming one year from today. What rate of return is built into the annuity?


A) 3.44%
B) 3.79%
C) 4.17%
D) 4.58%
E) 5.04%

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

Correct Answer

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A $150,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT?


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

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

Correct Answer

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Midway through the life of an amortized loan, the percentage of the payment that represents interest must be equal to the percentage that represents repayment of principal. This is true regardless of the original life of the loan or the interest rate on the loan.

A) True
B) False

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

Correct Answer

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Suppose a State of California bond will pay $1,000 eight years from now. If the going interest rate on these 8-year bonds is 5.5%, how much is the bond worth today?


A) $651.60
B) $684.18
C) $718.39
D) $754.31
E) $792.02

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

Correct Answer

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