A material supplier won a $5-$year contract to supply a construction company with all their building materials needs. The contract is expected to generate a first$-$year profit of $$12,000.$ This annual profit is expected to increase by $$7,000$ each successive year for the rest of the contract period. The profits will be invested in an account earning an interest rate of $8\%$ per year.

$($a$)$ Assuming that the profits are deposited in the account at the end of each year, how much money will be in the account immediately after the last deposit is made?

$($b$)$ What is the equivalent uniform annual deposit?

$($a$)$ The amount in the account immediately after the last deposit is $ $($to the nearest dollar$).$

$($b$)$ The equivalent uniform annual deposit is $ $($to the nearest dollar$)$