You start an annuity on your $18$th birthday. You deposit $$5$ at the end of every week until you

turn $65.$

$($a$)$ If your annuity earns $51$

$2\%$ interest, how much money will your have when you turn $65?$

$($b$)$ How much of that is interest?

$($c$)$ You$$re long lost rich relative decides to give you enough money to replace your annuity on

the previous page. How much money would they need to deposit now in order to save the

same amount as your annuity?