$($Comprehensive problem$)$ You would like to have $$79,000$ in $14$ years. To accumulate this amount, you plan to deposit an equal sum in the bank each year that will earn $10$

percent interest compounded annually. Your first payment will be made at the end of the year.

a$.$ How much must you deposit annually to accumulate this amount?

b$.$ If you decide to make a large lump$-$sum deposit today instead of the annual deposits, how large should the lump$-$sum deposit be$?($Assume you can earn $10$ percent on

this deposit.$)$

c$.$ At the end of year $5,$ you will receive $$10,000$ and deposit it in the bank in an effort to reach your goal of $$79,000$ at the end of year $14.$ In addition to the lump$-$sum deposit, how

much must you invest in $14$ equal annual deposits to reach your goal? $($Again$,$ assume you can earn $10$ percent on this deposit.$)$

b$.$ If you decide to make a large lump$-$sum deposit today instead of the annual deposits, how large should the lump$-$sum deposit be$?$

$$20,803\mathrm{.}17($Round to the nearest cent$)$

c$.$ If you deposit $$10,000$ received at the end of year $5$ in the bank, how much will it grow to in the account at the end of year $14?$

$$23579\mathrm{.}48($Round to the nearest cent.$)$

In addition to the lump$-$sum deposit, how much must you invest in $14$ equal annual deposits to reach your goal?

$($Round to the nearest cent.$)$