$2)$ A $$30,800$ loan at $8\%$ compounded quarterly is to be repaid by equal quarterly payments over a seven$-$year term.

a$.$ What will be the principal component of the sixth payment? $($Round your answer to the nearest cent.$)$

Principal

$3)$ An annuity providing a rate of return of $5\mathrm{.}5\%$ compounded monthly was purchased for $$52,000.$ The annuity pays $$470$ at the end of each month. How much of Payment $37$ will be interest? $($Do not round the intermediate calculations. Round your answer to the nearest cent.$)$

Interest $

$4)$ An annuity providing a rate of return of $6\mathrm{.}6\%$ compounded monthly was purchased for $$63,000.$ The annuity pays $$580$ at the end of each month. How much principal will be repaid in the fifth year? $($Do not round the intermediate calculations. Round your answer to the nearest cent.$)$

Principal repaid in the fifth year $

$5)$An annuity providing a rate of return of $4\mathrm{.}8\%$ compounded monthly was purchased for $$51,800.$ The annuity pays $$460$ at the end of each month.

e$.$ What will be the amount of the final payment? $($Round your answer to the nearest cent.$)$

Final payment $

$6)$A mortgage contract for $$48,400$ written $10$ years ago is just at the end of its second five$-$year term. The interest rates were $8\%$ compounded semiannually for the first term and $7\%$ compounded semiannually for the second term. If monthly payments throughout have been based on the original $25-$year amortization, calculate the principal balance at the end of the second term assuming the amortization period of $20$ years on renewal after the first five years. $($Round your answer to the nearest cent.$)$

Principal balance $

$7)$ 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

months.

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

Principal balance $