1. A saver places $1,000 in a certificate of deposit that matures after 20 years and that each year pays 4 percent interest, which is compounded annually until the certificate matures.
a) How much interest will the saver earn if the interest is left to accumulate?
b) How much interest will the saver earn if the interest is withdrawn each year?
c) Why are the answers to (a) and (b) different?
2. At the end of each year a self-employed person deposits $1,500 in a retirement ac-count that earns 7 percent annually.
a) How much will be in the account when the individual retires at the age of 65 if the contributions start when the person is 45 years old?
b) How much additional money will be in the account if the individual stops making the contribution at age 6S but defers retirement until age 70?
c) How much additional money will be in the account if the individual continues making the contribution but defers retirement until age 70?
d) Compare the answers to (b) and (c). What is the effect of continuing the contributions? How much is the difference between the two answers?
3. A saver wants $100,000 after ten years and believes that it is possible to earn an annual rate of 8 percent on invested funds.
a) What amount must be invested each year to accumulate $100,000 if (1) the pay-ments are made at the beginning of each year or (2) if they are made at the end of each year?
b) How much must be invested annually if the expected yield is only 5 percent?
4. Which is the better choice when purchasing a $30,000 car:
a) a four-year loan at 6 percent,
b) an immediate rebate of $2,000 and a four-year loan at 8 percent?
5. You are given the following information concerning two stocks:
|
A |
B |
| Expected return |
10% |
14% |
| Standard deviation of the expected return |
3.0 |
5.0 |
| Correlation coefficient of the returns |
-.1
|
a) What is the expected return on a portfolio consisting of 40 percent in stock A and 60 percent in stock B?
b) What is the standard deviation of this portfolio?
c) Discuss the risk and return associated with investing (a) all your funds in stock A, (b) all your funds in stock B, and (c) 40 percent in A and 60 percent in B. (This answer must use the numerical information in your answers derived above.)
6. What is the beta of a portfolio consisting of one share of each of the following stocks, given their respective prices and beta coefficients?
| Stock |
Price |
Beta |
| A |
$10 |
1.4 |
| B |
24 |
0.8 |
| C |
41 |
1.3 |
| D |
19 |
1.8 |
How would the portfolio beta differ if (a) the investor purchased 200 shares of stocks B and C for every 100 shares of A and D and (b) equal dollar amounts were invested in each stock?