Use PMT $=\frac{P(\frac{r}{n})}{[1-(1+\frac{r}{n}{)}^{-nt}]}$ to determine the regular payment amount, rounded to the nearest dollar. The price of a home is $$235,000.$ The bank requires a $20\%$ down payment and three points at the time of closing. The cost of the home is financed with a $30-$year fixed$-$rate mortgage at $7\mathrm{.}5\%.$ Complete parts $($a$)$ through $($e$)$ below below.

a$.$ Find the required down payment.

S

b$.$ Find the amount of the mortgage.

$

c$.$ How much must be paid for the three points at closing?

$($Round to the nearest dollar as needed.$)$

d$.$ Find the monthly payment $($excluding escrowed taxes and insurance$)$

$($Round to the nearest dollar as needed.$)$

e$.$ Find the totat cost of interest over $30$ years.

$($Round to the nearest dollar as needed$)$