11. (a) A man organizes to reimburse a $1,000 advance in 15 equivalent yearly portions. Interest is 4%. After his 10th instalment, he wishes to pay the equilibrium in a single amount. Accepting he can...

Extracted text: 11. (a) A man organizes to reimburse a $1,000 advance in 15 equivalent yearly portions. Interest is 4%. After his 10th instalment, he wishes to pay the equilibrium in a single amount. Accepting he can do this without an extra punishment premium, how much does he owe? (b) You are considering the purchase of a machine which will give you an annual return of $1,000 a year for 20 years. The return will be received uniformly and continuously over the years. How much can you pay for the machine and still obtain at least a 10 percent effective annual return on your investment in the machine?