9.1 [100] 

This problem explores the concept of Present Value in a variety of circumstances.

(a) [20] 

For the next 5 years, the prevailing interest rate is expected to be 6.5% per year, compounded quarterly. For the 5 years following that, the rate is expected to be 8.7% per year, compounded quarterly. Under these assumptions, what is the present value of a stream of 10 payments of $50,000 when they are received at the end of each year?

(b) [20] 

The interest rate assumptions of part (a) apply in this part (b) as well. Compute the present value of a stream of 40 payments of $12,500 when they arrive at the end of each quarter.

(c) [20] 

Again under the interest rate assumptions of part (a), compute the total present value of a stream of 40 payments paid at the end of each quarter, but of varying amounts: for the first three quarters of each year, the payments are $10,000 each. The last payment of each year is $20,000.

(d) [20] 

When you retire at age 65, you expect to live for another 20 years. During that time, you estimate that your living expenses will be $40,000 per year, and that the prevailing interest rate will be 12.0% per year, compounded quarterly. If you make identical withdrawals from your retirement account at the end of every quarter, what is the minimum amount of money that you must have in the account to meet your expenses over your expected lifetime?

(e) [20] 

You have an opportunity to purchase a small gold mine. Net income at the mine is estimated to be $100,000 per year. It's also estimated that mining can continue for 10 more years, and then the gold will be exhausted. Assuming that net income is realized only at year-end, and that you wish to make a 20% annual return on your investment, what would you be willing to pay for the mine?