years. To accumulate this amount, you plan to deposit an equal

sum in the bank each year that will earn $9$ percent interest

compounded annually. Your first payment will be made at the end

of the year.

a$.$ How much must you deposit alriually 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 $9$ percent on this deposit.$)$

c$.$ At the end of year $5,$ you will receive $$20,000$ and deposit it in

the bank in an effort to reach your goal of $$80,000$ at the end of

year $15.$ In addition to the lump$-$sum deposit, how much must you

invest in $15$ equal annual deposits to reach your goal? $($Again$,$

assume vou can earn $9$ dercent on this debosit.$)$