Present the intermediate calculations. Only final answers won't be considered.

a$)$ To renew the house, Ana got a loan of $$45,521$ that charged $8\%$ compounded quarterly. She agreed to make quarterly

payments for $3$ years.

$($i$)$ What is the size of the quarterly payment?

$($ii$)$ For the first payment, how much of the payment is interest?

$($iii$)$ For the first payment, how much of the loan principal is repaid?

$($iv$)$ After the first payment, how much of the loan remains to be paid?

$($v$)$ For the second payment, how much of the payment is interest?

$($vi$)$ For the second payment, how much of the loan principal is repaid?

$($vii$)$ After the second payment, how much of the loan remains to be paid?

$($viii$)$ How much is the last payment of the loan?

$($ix$)$ Construct an amortization schedule.

b$)$ To renew the house, Ana has negotiated with the bank to pay equally quarterly payments of $$4,305$ for $3$ years that charged

$8\%$ compounded quarterly. Answer the same questions $($i$)$ to $($ix$)$ as before.