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# Annual Rate or Return

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## Time Value of Money, Annual ROR, Interest, etc.

1. Compute the annual interest rate or rate of return that you will earn on the following investments:
a. A US T-Bill that has a current price of \$930 and will pay \$1000 at maturity six months from now.
b. A US T-Bill that has a current price of \$950 and will pay \$1000 at maturity six months from now.
c. A US Treasury note selling at its maturity value (\$1000), paying 9 percent coupon interest per year, and maturing in five years.
d. An acre of vacation property with a current price of \$5000 that you expect to be able to sell for \$6475 in three years. There are no other expenses or income from this property
e. A preferred stock with a current price of \$90 paying \$10.80 dividends per share per year forever

2. Compute the annual interest rate for the following investments:
a. A US T-Bill which which matures in ninety-one days with a quoted price of \$97.50 per \$100 maturity value.
b. A share of common stock purchased one year ago at a price of \$42 per share and just sold for \$48. No dividends were received.
c. A share of common stock purchased one year ago for \$21 and sold yesterday for \$18 after receipt of a dividend check for \$1
d. A share of common stock purchased for \$30 three years ago and just sold for \$30. Dividends of \$2.10 were received at the end of each of the three years of ownership.

3. Benito Rubio borrowed 5000 bolivars (B) from his older brother in Caracas, Venezuela. Benito promised to repay the loan in two-annual installments of B3000 each. What rate of interest is Benito paying his brother?

4. Determine the annual interest rate on the following debt contracts:
a. A \$25,000 mortgage with monthly payments of \$209.80 to be paid off in twenty-five years.
b. Solve the problem in (a) considering that the lender is charging a 2 percent fee at the time the loan is taken out so that the actual amount being lent to you is less than \$25,000.
c. An installment loan for \$2000 that has monthly payments of \$66 for the thirty-six months and an additional "balloon" payment of \$150 in the last month.

5. You are in the market for a new, high-performance windsurfing board. A dealer offers you financing on the \$1500 you need to buy the board at a "low 10 percent annual interest rate" for twenty-four months. Your payments are determined as follows:
a. Annual Interest = 10% of \$1500 = \$150 per year
Total Due = principal plus 2 years interest
= \$1500 + 2(\$150)
Monthly Payments = \$1800 / 24 months
= \$75 per month
- This procedure is called "add on" interest. What is the actual annual rate of interest being charged on this loan?

6. You need to borrow \$3000 to buy a powerboat. The boat dealer offers (low, low) monthly payments of \$99 for thirty - six months with an additional "balloon" payment of \$300 in the last month. What annual interest rate is the dealer charging you on the \$3000 loan?

7. Four years ago your mother invested \$10,000 in the Alpha Mutual Fund to provide money for your college education. All dividends were reinvested in the fund. Now the money is needed. The value of shares in the fund is \$14,116. What annual rate of return was earned on the original \$10,000 investment?

8. On January 16, 1990, Clara Hatfield invested \$2000 in the common stock of Ace Novelties. Ace pays dividends quarterly on April 15, July 15, October 15, and January 15 of each year. Clara sold her stock on July 16, 1991 after receiving \$30 dividends each quarter.
a. Suppose that Clara sold her Ace stock for \$1820. What annual rate of return did she earn?
b. Suppose that Clara sold her Ace stock for \$2000. What annual rate of return did she ear?
c. Suppose that Clara sold her Ace Stock for \$2194. What annual rate of return did she earn?

9. In December 1988, exactly four years ago, you purchased shares in a mutual fund for \$500. Although all the dividends were reinvested in the fund, you had to pay personal taxes at a rate of 20 percent on the dividends paid into you account each year. The current value of shares you own, including those obtained from dividend reinvestment, is \$705.80. If the shares are sold, you will be subject to a capital gains tax of 20 percent (capital gains = proceeds from sale - original cost of all shares). The dividends paid and reinvested are shown below.

b. If you sell all the shares now, what will be you after-tax rate of return?

Year 1989 1990 1991 1992
Dividends
\$ 30.00
\$ 32.00
\$ 36.00
\$ 40.00

10. Your father has asked your advice on the following problem. He has a mortgage loan on the family home that was made several years ago when the interest rate were lower. The loan has a current balance of \$40,000 and will be paid off in 20 years by paying \$330 per month. He has discussed paying off the loan ahead of schedule with an officer of the bank holding the mortgage. The bank is willing to accept \$36,000 right now to pay it off completely.
a. What interest rate, expressed as an annual rate, would your father earn by paying off the loan now rather than making monthly payments for 20 years.
b. Your father is currently earning 9 percent on his investments. Would if be worthwhile paying off the loan if he has the money available?

11. Two years ago Kareem Casey invested \$5000 in a savings certificate account with a seven-year (7) maturity and an annual interest rate of 9 percent compounded monthly. Interest rates are higher now and Kareem is considering withdrawing the current balance in the account and investing the money in a higher-yielding asset. However, the bank will deduct a "penalty for early withdrawal" equal to the first six-month' interest paid on the account.
a. What is the current balance in the account
b. What will be the balance at maturity, five years from now, if no withdrawals are made?
c. How much money will Kareem receive if he closes out the account now?
d. What interest rate must Kareem earn on an alternative investment to obtain as much money in five years' time as he would have by keeping the certificate?
e. If Kareem keeps the certificate for one more year, will the interest rate he must earn then to make withdrawal worthwhile be higher, lower, or the same as the rate calculated in d? Why?

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