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You are considering two equally risky annuities, each of which pays $25,000 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) 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.
B) A rational investor would be willing to pay more for DUE than for ORD, so their market prices should differ.
C) 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.
D) The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE.
E) The present value of ORD exceeds the present value of DUE, while the future value of DUE exceeds the future value of ORD.

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

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Your uncle has $300,000 invested at 7.5%, and he now wants to retire.He wants to withdraw $35,000 at the end of each year, beginning at the end of this year.He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account.What is the maximum number of $35,000 withdrawals that he can make and still have at least $25,000 left in the account? (Hint: If your solution for N is not an integer, round down to the nearest whole number.)


A) 12
B) 13
C) 14
D) 15
E) 16

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

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

A) True
B) False

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You are offered a chance to buy an asset for $7,250 that is expected to produce cash flows of $750 at the end of Year 1, $1,000 at the end of Year 2, $850 at the end of Year 3, and $6,250 at the end of Year 4.What rate of return would you earn if you bought this asset?


A) 4.93%
B) 5.19%
C) 5.46%
D) 5.75%
E) 6.05%

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

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The present value of a future sum increases 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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Which of the following statements is CORRECT?


A) 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.
B) A time line is not meaningful unless all cash flows occur annually.
C) Time lines are not useful for visualizing complex problems prior to doing actual calculations.
D) Time lines can be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly.
E) Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities.

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

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You want to buy new kitchen appliances 2 years from now, and you plan to save $8,200 per year, beginning one year from today.You will deposit your savings in an account that pays 6.2% interest.How much will you have just after you make the 2nd deposit, 2 years from now?


A) $15,260
B) $16,063
C) $16,908
D) $17,754
E) $18,642

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

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

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You sold your motorcycle 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 your motorcycle 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) B) and C)
G) All of the above

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Your father is considering purchasing an annuity that pays $5,000 at the beginning of each year for 5 years.He could earn 4.5% on his money in other investments with equal risk.What is the most he should pay for the annuity?


A) 20,701
B) $21,791
C) $22,938
D) $24,085
E) $25,289

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

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Southwestern Bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly.The loan (principal plus interest) must be repaid at the end of the year.Woodburn Bank also offers to lend you the $50,000, but it will charge an annual rate of 7.0%, with no interest due until the end of the year.How much higher or lower is the effective annual rate charged by Woodburn versus the rate charged by Southwestern?


A) 0.52%
B) 0.44%
C) 0.36%
D) 0.30%
E) 0.24%

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

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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

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What is the present value of the following cash flow stream at a rate of 6.25%? What is the present value of the following cash flow stream at a rate of 6.25%? A) $411.57 B) $433.23 C) $456.03 D) $480.03 E) $505.30


A) $411.57
B) $433.23
C) $456.03
D) $480.03
E) $505.30

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

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Your sister's pet supplies business obtained a 30-year amortized mortgage loan for $250,000 at a nominal annual rate of 7.0%, with 360 end-of-month payments.The firm can deduct the interest paid for tax purposes.What will the interest tax deduction be for for the first year of the loan? (Assume she took out the loan on January 1.)


A) $17,419.55
B) $17,593.75
C) $17,769.68
D) $17,947.38
E) $18,126.85

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

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Which of the following statements is CORRECT?


A) If CF0 is positive and all the other CFs are negative, then you cannot solve for I.
B) 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.
C) 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.
D) 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.
E) If you solve for I and get a negative number, then you must have made a mistake.

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

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You have $5,000 invested in a bank that pays 3.8% annually.How long will it take for your funds to triple?


A) 23.99
B) 25.26
C) 26.58
D) 27.98
E) 29.46

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

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Suppose United Bank offers to lend you $10,000 for one year at a nominal annual rate of 8.00%, but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year.What is the effective annual rate on the loan?


A) 8.24%
B) 8.45%
C) 8.66%
D) 8.88%
E) 9.10%

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

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Your bank offers a 10-year certificate of deposit (CD) that pays 6.5% interest, compounded annually.If you invest $2,000 in the CD, how much will you have when it matures?


A) $3,754.27
B) $3,941.99
C) $4,139.09
D) $4,346.04
E) $4,563.34

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

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What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,250?


A) $77.19
B) $81.25
C) $85.31
D) $89.58
E) $94.06

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

Correct Answer

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Which of the following statements is CORRECT?


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

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

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