Elkford Logging's bank will fix the interest rate on a $$60,000$ loan at $8\mathrm{.}1\%$ compounded monthly for the first four years. After four years, the interest rate will be fixed at the prevailing five$-$year rate. Monthly payments of $$800($except for a smaller final payment$)$ are required on the loan. $($Round your answers to $2$ decimal places.$)$

a$.$ If the interest rate after four years is $7\mathrm{.}5\%$ compounded monthly, when will the loan be paid off?

The loan will be paid off in

months

b$.$ What will be the amount of the final payment?

Final payment $

c$.$ What is the interest portion of the thirty$-$second payment?

Interest $

d$.$ Calculate the principal portion of the fifty$-$eighth payment.

Principal $