Response to the following problem:
You deposit $10,000 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 8 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 8 percent during the distribution period?
c. Repeat parts (a) and (b) above assuming earning rates of 7 percent and 9 percent during the deposit period and earning rates of 7 percent and 9 percent during the distribution period.