Question 1

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?

Accepted Answer

A)  A rational investor would be willing to pay more for DUE than for ORD, so their market prices should differ. 
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 ORD exceeds the present value of DUE, while the future value of DUE 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.

Question 2

How much would $5,000 due in 25 years be worth today if the discount rate were 5.5%?

Accepted Answer

A)  $1,067.95 
B)  $1,124.16 
C)  $1,183.33 
D)  $1,245.61 
E)  $1,311.17

Question 3

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?

Accepted Answer

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

Question 4

When a loan is amortized, a relatively high percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment's percentage declines in the loan's later years.

Accepted Answer

A) True 
 B)False

Question 5

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?

Accepted Answer

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

Question 6

What's the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded semiannually?

Accepted Answer

A)  $1,819 
B)  $1,915 
C)  $2,016 
D)  $2,117 
E)  $2,223

Question 7

Suppose the U.S. Treasury offers to sell you a bond for $747.25. No payments will be made until the bond matures 5 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price?

Accepted Answer

A)  4.37% 
B)  4.86% 
C)  5.40% 
D)  6.00% 
E)  6.60%

Question 8

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

Accepted Answer

A) True 
 B)False

Question 9

Which of the following statements is CORRECT?

Accepted Answer

A)  A time line is not meaningful unless all cash flows occur annually. 
B)  Time lines are useful for visualizing complex problems prior to doing actual calculations. 
C)  Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly. 
D)  Time lines cannot be constructed for annuities where the payments occur at the beginning of the periods. 
E)  Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven amounts.

Question 10

You have a chance to buy an annuity that pays $5,000 at the beginning of each year for 5 years. You could earn 4.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

Accepted Answer

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

Question 11

You plan to invest in bonds that pay 6.0%, compounded annually. If you invest $10,000 today, how many years will it take for your investment to grow to $30,000?

Accepted Answer

A)  12.37 
B)  13.74 
C)  15.27 
D)  16.97 
E)  18.85

Question 12

Your child's orthodontist offers you two alternative payment plans. The first plan requires a $4,000 immediate up-front payment. The second plan requires you to make monthly payments of $137.41, payable at the end of each month for 3 years. What nominal annual interest rate is built into the monthly payment plan?

Accepted Answer

A)  12.31% 
B)  12.96% 
C)  13.64% 
D)  14.36% 
E)  15.08%

Question 13

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

Accepted Answer

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

Question 14

Which of the following statements regarding a 15-year (180-month) $125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)

Accepted Answer

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.

Question 15

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?

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

Your uncle is about to retire, and he wants to buy an annuity that will provide him with $75,000 of income a year for 20 years, with the first payment coming immediately. The going rate on such annuities is 5.25%. How much would it cost him to buy the annuity today?

Accepted Answer

A)  $825,835 
B)  $869,300 
C)  $915,052 
D)  $963,213 
E)  $1,011,374

Question 18

Riverside 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. Midwest 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 Midwest versus the rate charged by Riverside?

Accepted Answer

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

Question 19

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

Question 20

What is the present value of the following cash flow stream at a rate of 8.0%?

Accepted Answer

A)  $7,917 
B)  $8,333 
C)  $8,772 
D)  $9,233 
E)  $9,695

Exam 5: Time Value of Money