$($Comprehensive problem$)$ You would like to have $$59,000$ in $12$ 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 this lump$-$sum deposit be$?($Assume you can earn $10$ percent on this deposit.$)$

c$.$ At the end of five years, you will receive $$15,000$ and deposit this in the bank toward your goal of $$59,000$ at the end of year $12.$ In addition to the lump$-$sum deposit, how much must you deposit in equal annual amounts, beginning in year $1$ to reach your goal? $($Aqain$,$ assume vou can earn $10$ percent on vour deposits.$)$

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

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