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 \( \$ 114,000 \). 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. \( \$ 22,800 \) b. Find the amount cf the mortgage. \( \$ 91,200 \) c. How much must be paid for the three points at closing? \( \$ \square \) (Round to the nearest dollar as needed.)

To calculate the cost of three points at closing, we first need to understand that one point is equal to 1% of the mortgage amount. Since your mortgage amount is \( \$ 91,200 \), three points would be 3% of that amount. Calculating it: \[ \text{Cost of Points} = 3\% \times 91,200 = 0.03 \times 91,200 = 2,736 \] So, the amount that must be paid for the three points at closing is approximately \( \$ 2,736 \). Now, just a little insight into mortgages: Many people overlook the impact of points on the overall cost of a mortgage. Paying points upfront can lower your monthly payment, but it's important to calculate how long you plan to stay in the home to determine if it's worth it!