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.

Complete this question by entering your answers in the tabs below.

Req A and $B$

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. $($Do not round intermediate calculations. Round your answers to $2$

decimal places. $($e$.$g$.,32\mathrm{.}19))$