The price of a condominium is $\$ 182,000$. 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 $6.5 \%$. Use the following formula to determine the regular payment amount. Complete parts (a) through (e) below.
\[
P M T=\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]}
\]
a. Find the required down payment.
\[
\$ 9100
\]
b. Find the amount of the mortgage.
\[
\$ 172,900
\]
c. How much must be paid for the one point at closing?
$\$ \square$
(Round to the nearest dollar as needed.)

Step 1 ：The price of a condominium is $182,000. 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 6.5%.

Step 2 ：First, we need to find the required down payment. This is 5% of the price of the condominium. So, the down payment is $9100.

Step 3 ：Next, we need to find the amount of the mortgage. This is the price of the condominium minus the down payment. So, the amount of the mortgage is $172,900.

Step 4 ：Finally, we need to find out how much must be paid for the one point at closing. One point is equivalent to 1% of the mortgage amount. Therefore, to find the amount to be paid for the one point at closing, we need to calculate 1% of the mortgage amount which is $172,900.

Step 5 ：After calculating, we find that the amount to be paid for the one point at closing is $1729.

Step 6 ：\(\boxed{\text{The amount to be paid for the one point at closing is \$1729.}}\)