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

you can earn $8$ percent on this deposit.$)$

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

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

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$?$

$$23643\mathrm{.}13($Round to the nearest cent.$)$

c$.$ If you deposit $$20,000$ received at the end of year $5$ in the bank, how much will it grow to in the account at the end of year $15?$

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