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 $$ 7.5 \% $$. Use the following formula to determine the regular payment amount. Complete parts (a) through (e) below. $$ \text { PMT }=\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]} $$ b. Find the amount of the mortgage. $$ \$ 104,500 $$ c. How much must be paid for the one point at closịg? $$ \$ 1,045 $$ (Round to the nearest dollar as needed.) d. Find the monthly payment (excluding escrowed taxes and insurance). $$ \$ 731 $$ (Round to the nearest dollar as needed.) e. Find the total cost of interest over 30 years. $$ \$ \square $$ (Round to the nearest dollar as needed.)

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**Step 1. Calculate the Total Amount Paid Over the Life of the Loan**

The monthly payment is given as  
$$
\text{PMT} = 731.
$$  
Since the loan term is 30 years and payments are made monthly, the total number of payments, $$ n \times t $$, is  
$$
12 \times 30 = 360.
$$  
Thus, the total amount paid is  
$$
731 \times 360 = 263\,160.
$$

**Step 2. Determine the Total Interest Paid**

The mortgage amount (the principal) is  
$$
P = 104\,500.
$$  
The total interest paid over 30 years is the total amount paid minus the principal. That is,  
$$
\text{Total Interest} = 263\,160 - 104\,500 = 158\,660.
$$

Thus, the total cost of interest over 30 years is  
$$
\$158\,660.
$$
The total cost of interest over 30 years is \$158,660.

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