Holly Kresch is thinking of buying a home for $$263,600.$ State Bank advertises an $80\%,$ thirty$-$year simple interest amortized loan at $6\mathrm{.}25\%$ interest, with an APR of $7\mathrm{.}13\%.$ Boonville Savings and Loan advertises an $80\%,$ thirty$-$year simple interest amortized loan at

$6\mathrm{.}5\%$

interest with an APR of $7\mathrm{.}27\%.($Round your answers to the nearest cent.$)$

$($a$)$ Find Holly's monthly payment if she borrows through State Bank.

$($b$)$ Find Holly's monthly payment if she borrows through Boonville Savings and Loan.

$($c$)$ Use the APR to approximate the fees included in the finance charge by State Bank.

$($d$)$ Use the APR to approximate the fees included in the finance charge by Boonville Savings and Loan.