Wayne$-$Powers has purchased a fleet of delivery vehicles for $$200,000$ with a

$10\%$ down payment. The remainder of the debt is to be amortized via semi$-$annual

payments of $$15,000($except for one smaller final payment$).$ Interest on the debt is

$8\mathrm{.}1\%$ compounded monthly.

a$)$ How long will this debt take to pay?

b$)$ How much of the $4$th payment will go towards reducing principal?

c$)$ Determine the size of the final payment.