BU4762 Sample Midterm #1

1. A 2-year, $13,500 mortgage has a $ 1,282.20 monthly payment. What will be the remaining balance on the mortgage after 3 months?

2. You have the opportunity to buy a perpetuity that pays $1,000 annually. Your required rate of return on this investment is 15 percent. You should be essentially indifferent to buying or not buying the investment if it were offered at a price of

3. Frank Lewis has a 30-year, $100,000 mortgage with a nominal interest rate of 10 percent and monthly compounding. Which of the following statements regarding his mortgage is most correct?

a. The monthly payments will decline over time.

b. The proportion of the monthly payment that represents interest will be lower for the last payment than for the first payment on the loan.

c. The total dollar amount of principal being paid off each month gets larger as the loan approaches maturity.

d. Statements a and c are correct.

5. Statements b and c are correct.

4. An investment pays you 9 percent interest compounded semiannually. A second investment of equal risk, pays interest compounded quarterly. What nominal rate

of interest would you have to receive on the second investment in order to make you indifferent between the two investments?

5. You want to borrow $1,000 from a friend for one year, and you propose to pay her $1,120 at the end of the year. She agrees to lend you the $1,000, but she wants you to pay her $10 of interest at the end of each of the first 11 months plus $1,010 at the end of the 12th month. How much higher is the effective annual rate under your friends proposal than under your proposal?

6. Elizabeth has $35,000 in an investment account. Her goal is to have the account grow to $100,000 in 10 years without having to make any additional contributions to the account. What effective annual rate of interest would she need to earn on the account in order to meet her goal?

7. You are considering buying a new car. The sticker price is $15,000 and you have $2,000 to put toward a down payment. If you can negotiate a nominal annual interest rate of 12 percent and you wish to pay for the car over a 2.5-year period, what are your monthly car payments?

8. Your uncle has agreed to deposit $3,000 in your brokerage account at the beginning of each of the next five years (t=0, 1, 2, 3, and 4). Your estimate that you can earn 9 percent a year on your investments. How much will you have in your account four years for now (at t=4)? Assume that no money is withdrawn form the account until t=4)

9. South Penn Trucking is financing a new truck with a loan of $10,000 to be repaid in 5 annual end-of-year installments of $2,504.56. What annual interest rate is the company paying?

10. Which of the following investments would provide an investor the highest effective annual return?

1. An investment that has a 9 percent nominal rate with semiannual com-pounding.
2. An investment that has a 9 percent nominal rate with quarterly com-pounding.
3. An investment that has a 9.2 percent nominal rate with annual com-pounding.
4. An investment that has an 8.9 percent nominal rate with monthly com-pounding.
5. An investment that has an 8.9 percent nominal rate with quarterly compounding.

11. You recently received a letter from Cut-to-the-Chase National Bank that offers you a new credit card that has no annual fee. It states that the annual percentage rate (APR) is 18% on outstanding balances. What is the effective annual interest rate? (Hint: Remember these companies bill you monthly)

12. Suppose you put $100 into a savings account today, the account pays a nominal annual interest rate of 6 percent, but compounded semiannually, and you withdraw $100 after 6 months. What would your ending balance be 20 years after the initial $100 deposit was made?

13. You are willing to pay $15,625 to purchase a perpetuity that will pay you and your heirs $1,250 each year, forever. If your required rate of return does not change, how much would you be willing to pay if this were a 20-year annual payment, ordinary annuity instead of a perpetuity?

14. You have just borrowed $20,000 to buy a new car. The loan agreement calls for 55 monthly payments of $474.53 each to begin one month from today. If the interest is compounded monthly, then what is the effective annual rate on this loan?

15. In 1626, Dutchman Peter Minuit purchased Manhattan Island from a local Native American tribe. Historians estimate that the price he paid for the island was about $24 worth of goods, including beads, trinkets, close, kettles and axe heads. Many people find it laughable that Manhattan Island would be sold for $24, but you need to consider the future value (FV) of that price in more current times. If the $24 purchase price could have been invested at a 6% annual interest rate, what is its value as of 2017 (391 years later)?