1. (Solving for r of an annuity) You lend a friend $25,000 which your friend will repay in 15 equal annual end-of-year payments of $3,000 with the first payment to be received 1 year from now. What rate of return does your loan receive?

2. You lend a friend $13,000 for which your friend will repay you $80,000 at the end of 13 years. What interest rate are you charging your friend?

3. You would like to have $54,000 in 10 years. To accumulate this amount, you plan to deposit each year an equal sum in the bank, which will earn 7 percent interest compounded annually. Your first payment will be made at the end of the year.

a. How much must you deposit annually to accumulate this amount?

b. If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should this lump-sum deposit be? (Assume you can earn 7 percent on this deposit.)

c. At the end of 5 years, you will receive $9,000 and deposit this in the bank toward your goal of $54,000 at the end of 10 years. In addition to this deposit, how much must you deposit in equal annual deposits to reach your goal? (Again assume you can earn 7 percent on this deposit.)