Use PMT $=\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]}$ to determine the regular payment amount, rounded to the nearest dollar. The price of a home is $\$ 156,000$. 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 $9 \%$. Complete parts (a) through (e) below. a. Find the required down payment. 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). $\$ \square$ (Round to the nearest dollar as needed.) ๑. Find the total cost of interest over 30 years. (Round to the nearest dollar as needed.)

Step 1 ：Calculate the down payment, which is 20% of the home price. So, \(\text{down payment} = 0.2 \times 156000 = \$31200\).

Step 2 ：Calculate the amount of the mortgage, which is the home price minus the down payment. So, \(\text{mortgage} = 156000 - 31200 = \$124800\).

Step 3 ：Calculate the cost of the three points at closing, which is 3% of the amount of the mortgage. So, \(\text{points} = 0.03 \times 124800 = \$3744\).

Step 4 ：Calculate the monthly payment using the PMT formula. The principal P is the amount of the mortgage, the rate r is 9%, the number of periods n is 12 (since payments are monthly), and the time t is 30 years. So, \(\text{PMT} = \frac{124800 \times (0.09/12)}{1 - (1 + 0.09/12)^{-12 \times 30}} = \$1004\).

Step 5 ：Calculate the total cost of interest over 30 years. This is the total amount paid over 30 years (monthly payment times number of months) minus the amount of the mortgage. So, \(\text{total interest} = (1004 \times 12 \times 30) - 124800 = \$236701\).

Step 6 ：\(\boxed{\text{a. The required down payment is } \$31200}\)

Step 7 ：\(\boxed{\text{b. The amount of the mortgage is } \$124800}\)

Step 8 ：\(\boxed{\text{c. The cost of the three points at closing is } \$3744}\)

Step 9 ：\(\boxed{\text{d. The monthly payment (excluding escrowed taxes and insurance) is } \$1004}\)

Step 10 ：\(\boxed{\text{e. The total cost of interest over 30 years is } \$236701}\)