The Roths bought a house for $$437,800.$ They paid the sellers a $20\%$ down payment and obtained a simple interest amortized

loan for the balance from their bank for the remainder, at $4\frac{7}{8}\%$ for thirty years. The bank in turn paid the sellers the loan

amount, less a $6\%$ sales commission paid to the sellers' and buyers' real estate agents. The bank charged them $2$ points plus

fees totaling $$8,535\mathrm{.}50$; of these fees, $$6,307\mathrm{.}47$ were included in the finance charge.

$($a$)$ Find the loan amount.

$$|$

$($b$)$ Find the "legal loan amount" $-$the amount borrowed, according to the Truth in Lending Act. $($Round your answer to

the nearest cent.$)$

$

$($c$)$ Find the Roth's monthly payment. $($Round your answer to the nearest cent.$)$

$

$($d$)$ Find the APR $($round to the nearest hundredth of $1\%).$

$\%$

$($e$)$ Find the total interest paid. $($Round your answer to the nearest cent.$)$

$

$($f$)$ Find the total finance charge. $($Round your answer to the nearest cent.$)$

$

$($g$)$ Find the amount that the sellers are paid for their house.

$