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Farmers Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly. Merchants Bank offers to lend you the $50,000, but it will charge 6.0%, simple interest, with interest paid at the end of the year. What's the difference in the effective annual rates charged by the two banks?


A) 1.56%
B) 1.30%
C) 1.09%
D) 0.91%
E) 0.72%

F) All of the above
G) None of the above

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

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

A) True
B) False

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What is the PV of an ordinary annuity with 5 payments of $4,700 if the appropriate interest rate is 4.5%?


A) $16,806
B) $17,690
C) $18,621
D) $19,601
E) $20,633

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

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What is the PV of an annuity due with 5 payments of $2,500 at an interest rate of 5.5%?


A) $11,262.88
B) $11,826.02
C) $12,417.32
D) $13,038.19
E) $13,690.10

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

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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 FV of the negative CFs. It is impossible to find the value of I without a computer or financial calculator.
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 can still solve for I.

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

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Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but with equal end-of-month payments. What percentage of the 2nd monthly payment will go toward the repayment of principal?


A) 73.67%
B) 77.55%
C) 81.63%
D) 85.93%
E) 90.45%

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

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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 greater the percentage of the payment that will be a repayment of principal.

A) True
B) False

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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) None of the above
G) A) and E)

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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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You plan to invest in securities that pay 8.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20?


A) 5.14
B) 5.71
C) 6.35
D) 7.05
E) 7.84

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

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Bob has $2,500 invested in a bank that pays 4% annually. How long will it take for his funds to double?


A) 14.39
B) 15.15
C) 15.95
D) 16.79
E) 17.67

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

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Pace Co. borrowed $20,000 at a rate of 7.25%, simple interest, with interest paid at the end of each month. The bank uses a 360-day year. How much interest would Pace have to pay in a 30-day month?


A) $120.83
B) $126.88
C) $133.22
D) $139.88
E) $146.87

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

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Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the beginning of each of the next 20 years?


A) $22,598.63
B) $23,788.03
C) $25,040.03
D) $26,357.92
E) $27,675.82

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

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

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Suppose you are buying your first condo for $145,000, and you will make a $15,000 down payment. You have arranged to finance the remainder with a 30-year, monthly payment, amortized mortgage at a 6.5% nominal interest rate, with the first payment due in one month. What will your monthly payments be?


A) $741.57
B) $780.60
C) $821.69
D) $862.77
E) $905.91

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

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Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years?


A) $28,532
B) $29,959
C) $31,457
D) $33,030
E) $34,681

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

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You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning one year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the 3rd deposit, 3 years from now?


A) $11,973
B) $12,603
C) $13,267
D) $13,930
E) $14,626

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

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

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