The interest rate for the first three years of an $$91,500$ mortgage is $4\mathrm{.}4\%$ compounded semiannually. Monthly payments are based on a

$20-$year amortization. If a $$5,800$ prepayment is made at the end of the sixteenth month.

a$.$ How much will the amortization period be shortened?

The amortization period will be shortened by $16$ months.

b$.$ What will be the principal balance at the end of the three$-$year term? $($Round your answer to the nearest cent.$)$