12. Selyn Cohen is 63 years old and recently retired. He wishes to provide retirement income for himself and is considering an annuity contract with the Philo Life Insurance Company. Such a contract pays him an cqual-dollar amount each year that he lives. For this cash-flow stream, he must put up a specific amount of money at the beginning. According to actuary tables, his life expectancy is 15 years, and that is the duration on which the insurance company bases its calculations regardless of how long he actually lives. a. If Philo Life uses a compound annual interest rate of 5 percent in its calculations, what must Cohen pay at the outset for an annuity to provide him with $10,000 per year? (Assume that the expected annual payments are at the end of each of the 15 years.) b. What would be the purchase price if the compound annual interest rate is 10 percent? c. Cohen had $30,000 to put into an annuity. How much would he receive cach year if the insurance company uses a 5 percent compound annual interest rate in its calcula- tions? A 10 percent compound annual interest rate? The Happy Hang Glide Company is purchasing a building and has obtained a $190,000 mortgage loan for 20 years. The loan bears a compound annual interest rate of 17 percent and calls for equal annual installment payments at the end of each of the 20 years. What is the amount of the annual payment? 14. Establish loan amortization schedules for the following loans to the nearest cent (see Table 3.8 for an example): a. A 36-month loan of $8,000 with equal installment payments at the end of each month. The interest rate is 1 percent per month. b. A 25-year mortgage loan of $184,000 at a 10 percent compound annual interest rate with equal instaliment payments at the end of each year. 15. You have borrowed $14,300 at a compound annual interest rate of 15 percent. You feel that you will be able to make annual payments of $3,000 per year on your loan. (Payments include both principal and interest.) How long will it be before the loan is entirely paid off (to the nearest year)? 16. Lost Dutchman Mines, Inc., is considering investing in Peru. It makes a bid to the gov- ernment to participate in the development of a mine, the profits of which will be realized at the end of five years. The mine is expected to produce $5 million in cash to Lost Dutchman Mines at that time. Other than the bid at the outset, no other cash flows will occur, as the government will reimburse the company for all costs. If Lost Dutchman requires a nominal annual return of 20 percent (ignoring any tax consequences), what is the maximum bid it should make for the participation right if interest is compounded (a) annually? () semiannually? (c) quarterly? (d) continuously? 17