The price of a condominium is $$110,000.$ The bank requires a $5\%$ down payment and one point at the time of closing. The cost of the condominium is financed with a $30-$year fixed$-$rate mortgage at $7\mathrm{.}5\%.$ Use the following formula to determine the regular payment amount. Complete parts $($a$)$ through $($e$)$ below.

$PMT=\frac{P(\frac{r}{n})}{[1-(1+\frac{r}{n}{)}^{-nt}]}$

a$.$ Find the required down payment.