Question 1

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. For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?

Accepted Answer

A)  14.96 
B)  15.71 
C)  16.49 
D)  17.32

Question 2

Suppose a bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments of $250.00 at the end of each quarter and then pay off the principal amount at the end of the year. What is the effective annual rate on the loan?

Accepted Answer

A)  8.46% 
B)  9.37% 
C)  9.86% 
D)  10.38%

Question 3

Suppose you borrowed $12,000 at a rate of 9% and must repay it in 4 equal installments at the end of each of the next 4 years. How much would your payments be?

Accepted Answer

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

Question 4

A $50,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is correct?

Accepted Answer

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 lower if the interest rate were lower. 
D)  The last payment would have a higher proportion of interest than the first payment.

Question 5

Your uncle has $500,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $40,000 at the beginning of each year, beginning immediately. How many years will it take to exhaust his funds, i.e., run the account down to zero?

Accepted Answer

A)  24.38 
B)  25.66 
C)  27.01 
D)  28.44

Question 6

Your aunt is about to retire, and she wants to buy an annuity that will provide her with $65,000 of income a year for 25 years, with the first payment coming immediately. The going rate on such annuities is 6.25%. How much would it cost her to buy the annuity today?

Accepted Answer

A)  $739,281.38 
B)  $778,190.93 
C)  $819,148.35 
D)  $862,261.42

Question 7

When inputting information into a financial calculator, one of the cash flow components must be negative since the calculator is set up to solve an equation equal to zero.

Accepted Answer

A) True 
 B)False

Question 8

John and Daphne are saving for their daughter Ellen's university education. Ellen is now 10 years old and will be entering university 8 years from now (t = 8). University tuition and expenses at City U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. John and Daphne expect Ellen to graduate in four years. (If Ellen wants to go to graduate school, she will be on her own.) Tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and 11). So far, John and Daphne have accumulated $15,000 in the university savings account. Their long-run financial plan is to add an additional $5,000 at the beginning of each of the next 4 years (at t = 0, 1, 2, and 3). Then they plan to make four equal annual contributions at the end of each of the following five years (t = 4, 5, 6, 7, and 8). They expect their investment account to earn 9%. How large must the annual payments be at t = 4, 5, 6, 7, and 8 to meet Ellen's anticipated university costs?

Accepted Answer

A)  $818.91 
B)  $862.01 
C)  $907.38 
D)  $955.13

Question 9

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?

Accepted Answer

A)  $28,532.45 
B)  $29,959.08 
C)  $31,457.03 
D)  $33,029.88

Question 10

You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning?

Accepted Answer

A)  7.62% 
B)  8.00% 
C)  8.40% 
D)  8.82%

Question 11

You plan to invest in securities that pay 9.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment account to grow to $9,140.20?

Accepted Answer

A)  4.59 
B)  5.10 
C)  6.30 
D)  7.00

Question 12

How many years would it take $50 to triple if it were invested in a bank that pays 3.8% per year?

Accepted Answer

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

Question 13

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.

Accepted Answer

A) True 
 B)False

Question 14

What's the present value of $1,525 discounted back 5 years if the appropriate interest rate is 6%, compounded monthly?

Accepted Answer

A)  $969.34 
B)  $1,020.36 
C)  $1,074.06 
D)  $1,130.59

Question 15

Suppose you borrowed $12,000 at a rate of 9% and must repay it in 4 equal installments at the end of each of the next 4 years. How much interest would you have to pay in the first year?

Accepted Answer

A)  $925.97 
B)  $974.70 
C)  $1,026.00 
D)  $1,080.00

Question 16

What is the PV of an annuity due with 10 payments of $2,700 at an interest rate of 6.5%?

Accepted Answer

A)  $20,671.48 
B)  $21,705.06 
C)  $22,790.31 
D)  $23,929.82

Question 17

Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is correct?

Accepted Answer

A)  The periodic rate of interest is 1.5% and the effective rate of interest is 3%. 
B)  The periodic rate of interest is 6% and the effective rate of interest is greater than 6%. 
C)  The periodic rate of interest is 1.5% and the effective rate of interest is greater than 6%. 
D)  The periodic rate of interest is 3% and the effective rate of interest is 6%.

Question 18

What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 6.5%?

Accepted Answer

A)  $16,641.51 
B)  $17,517.38 
C)  $18,439.35 
D)  $19,409.84

Question 19

An investment costs $1,000 (CF at t = 0) and is expected to produce cash flows of $75 at the end of each of the next 5 years, then an additional lump sum payment of $1,000 at the end of the 5th year. What is the expected rate of return on this investment?

Accepted Answer

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

Question 20

Suppose you have $1,500 and plan to purchase a 5-year certificate of deposit (CD) that pays 3.5% interest, compounded annually. How much will you have when the CD matures?

Accepted Answer

A)  $1,781.53 
B)  $1,870.61 
C)  $1,964.14 
D)  $2,062.34

Exam 4: Time Value of Money