$($Compounding using a calculator$)$ Bart Simpson, age $9,$ wants to be able to buy a really cool new car when he turns $18.$ His really cool car costs $$15,000$ today, and its cost is expected to increase $2$ percent annually. Bart wants to make one deposit today $($he can sell his mint$-$condition original Nuclear Boy comic book$)$ into an account paying $7\mathrm{.}3$ percent annually in order to buy his car in $9$ years. How much will Bart's car cost, and how much does Bart have to save today in order to buy this car at age $18?$

a$.$ How much will Bart's car cost after $9$ years?

$($Round to the nearest cent$)$

b$.$ How much does Bart have to save today in order to buy this car at age $18?$

$($Round to the nearest cent$)$