$7.$ A $$37,000$ loan at $8\mathrm{.}2\%$ compounded semiannually is to be repaid by semiannual payments of $$2500($except for the smaller final payment$).$

a$)$ What will be the principal component of the $16$th payment?

b$)$ What will be the interest portion of the $6$th payment?

c$)$ How much will payments $8$ to $14$ inclusive reduce the principal balance?

d$)$ How much interest will be paid in the $5$th year?

e$)$ What will be the final payment?