You deposit $11,000 annually into a life insurance fund for the next 10 years, after which time you plan to retire. a. If the deposits are made at the beginning of the year and earn an interest rate of 7 percent, what will be the amount in the retirement fund at the end of year 10? b. Instead of a lump sum, you wish to receive annuities for the next 20 years (years 11 through 30). What is the constant annual payment you expect to receive at the beginning of each year if you assume an interest rate of 7 percent during the distribution period? c. Repeat parts (a) and (b) above assuming earning rates of 6 percent and 8 percent during the deposit period and earning rates of 6 percent and 8 percent during the distribution period. a. Suppose a 65-year-old person wants to purchase an annuity from an insurance company that would pay $22,000 per year until the end of that person's life. The insurance company expects this person to live for 15 more years and would be willing to pay 7 percent on the annuity. How much should the insurance company ask this person to pay for the annuity? b. A second 65-year-old person wants the same $22,000 annuity, but this person is healthier and is expected to live for 20 more years. If the same 7 percent interest rate applies, how much should this healthier person be charged for the annuity? c. In each case, what is the new purchase price of the annuity if the distribution payments are made at the beginning of the year? (For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))