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 \( \$ 183,000 \). 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 \( 10 \% \). Complete parts (a) through (e) below. a. Find the required down payment. \( \$ 36,600 \) b. Find the amount of the mortgage. \( \$ 146,400 \) c. How much must be paid for the three points at closing? \( \$ \square \) (Roundfo the nearest dollar as needed.)

To find the amount to be paid for the three points at closing, first, we need to clarify what points are. Points are fees paid to the lender at closing that decrease the interest rate over the life of the mortgage, typically representing one percent of the loan amount each. In this case, three points would be calculated on the amount of the mortgage. Given that the mortgage amount is \( \$146,400 \), the cost for three points is calculated as follows: \[ \text{Cost of three points} = \text{Mortgage Amount} \times \text{Points Rate} \] \[ \text{Cost of three points} = \$146,400 \times 0.03 = \$4,392 \] Thus, the amount to be paid for the three points at closing is \( \$4,392 \) after rounding to the nearest dollar.