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Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year?


A) $2,404.91
B) $2,531.49
C) $2,658.06
D) $2,790.96
E) $2,930.51

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

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A U.S. Treasury bond will pay a lump sum of $1,000 exactly 3 years from today. The nominal interest rate is 6%, semiannual compounding. Which of the following statements is CORRECT?


A) The periodic interest rate is greater than 3%.
B) The periodic rate is less than 3%.
C) The present value would be greater if the lump sum were discounted back for more periods.
D) The present value of the $1,000 would be smaller if interest were compounded monthly rather than semiannually.
E) The PV of the $1,000 lump sum has a higher present value than the PV of a 3-year, $333.33 ordinary annuity.

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

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You want to quit your job and return to school for an MBA degree 3 years from now, and you plan to save $7,000 per year, beginning immediately. You will make 3 deposits in an account that pays 5.2% interest. Under these assumptions, how much will you have 3 years from today?


A) $20,993
B) $22,098
C) $23,261
D) $24,424
E) $25,645

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

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After graduation, you plan to work for Dynamo Corporation for 12 years and then start your own business. You expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t = 6) and $15,000 annually for the following 6 years (t = 7 through t = 12) . The first deposit will be made a year from today. In addition, your grandfather just gave you a $25,000 graduation gift which you will deposit immediately (t = 0) . If the account earns 9% compounded annually, how much will you have when you start your business 12 years from now?


A) $238,176
B) $250,712
C) $263,907
D) $277,797
E) $291,687

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

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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 C)
G) All of the above

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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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Your father paid $10,000 (CF at t = 0) for an investment that promises to pay $750 at the end of each of the next 5 years, then an additional lump sum payment of $10,000 at the end of the 5th year. What is the expected rate of return on this investment?


A) 6.77%
B) 7.13%
C) 7.50%
D) 7.88%
E) 8.27%

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

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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 B)
G) A) and C)

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Your 75-year-old grandmother expects to live for another 15 years. She currently has $1,000,000 of savings, which is invested to earn a guaranteed 5% rate of return. If inflation averages 2% per year, how much can she withdraw (to the nearest dollar) at the beginning of each year and keep the withdrawals constant in real terms, i.e., growing at the same rate as inflation and thus enabling her to maintain a constant standard of living?


A) $65,632
B) $72,925
C) $81,027
D) $89,130
E) $98,043

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

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

Correct Answer

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How much would $100, growing at 5% per year, be worth after 75 years?


A) $3,689.11
B) $3,883.27
C) $4,077.43
D) $4,281.30
E) $4,495.37

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

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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 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) All of the above
F) None of the above

Correct Answer

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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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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

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

Correct Answer

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Last year Ellis 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 Ellis' EPS to triple?


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

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

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Which of the following statements is CORRECT?


A) If you have a series of cash flows, each of which is positive, you can solve for I, where the solution value of I causes the PV of the cash flows to equal the cash flow at Time 0.
B) If you have a series of cash flows, and CF0 is negative but each of the following CFs is positive, you can solve for I, but only if the sum of the undiscounted cash flows exceeds the cost.
C) To solve for I, one must identify the value of I that causes the PV of the positive CFs to equal the absolute value of the PV of the negative CFs. This is, essentially, a trial-and-error procedure that is easy with a computer or financial calculator but quite difficult otherwise.
D) If you solve for I and get a negative number, then you must have made a mistake.
E) If CF0 is positive and all the other CFs are negative, then you cannot solve for I.

F) None of the above
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

Correct Answer

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Which of the following statements is CORRECT?


A) The present value of a 3-year, $150 ordinary annuity will exceed the present value of a 3-year, $150 annuity due.
B) If a loan has a nominal annual rate of 8%, then the effective rate will never be less 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) All of the above
G) None of the above

Correct Answer

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