Suppose that you are purchasing a house $($loan amount$=$$$200,000)$ and inquire about the terms for a $30-$year fixed$-$rate mortgage. You are given the following two quotes:

Loan # A:

Annual interest rate of $3\mathrm{.}75\%$ with monthly payments and compounding

No discount points

Origination fee of $0\mathrm{.}75\%$

$$928$ in third$-$party closing costs

Loan # B:

Annual interest rate of $3\mathrm{.}625\%$ with monthly payments and compounding

$1\mathrm{.}25$ discount points

Origination fee of $1\%$

$$18$ in third$-$party closing costs

$($Enter the answer as a positive number and round your answer to $2$ decimals. Also, report the effective borrowing cost without the percentage sign. For example if your calculated EBC is $5,$ record your answer as $5\mathrm{.}00)$

a$)$ What is the remaining mortgage balance at the end of third year for Loan A$?$

b$)$ What is the remaining mortgage balance at the end of third year for Loan B$?$