Use PMT \( =\frac{P\left(\frac{p}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]} \) 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. b. Find the amount of the mortgage. \( \$ 91,200 \) c. How much must be paid for the three points at closing? \( \$ 2,736 \) (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.)

To find the regular payment amount using the PMT formula, you first need to determine the mortgage amount and then apply the given data into the formula. Plugging in the values: The principal \( P \) is \( 91,200 \) (the mortgage amount). The annual interest rate \( r \) is \( 0.10 \) (10%). The number of payments per year \( n \) is \( 12 \) (monthly payments). The total number of payments \( t \) is \( 30 \) years. Now, let's calculate: 1. **Find the monthly interest rate**: \( \frac{p}{n} = \frac{0.10}{12} = 0.0083333 \) 2. **Find the total number of payments**: \( n \times t = 12 \times 30 = 360 \) 3. **Plugging values into the PMT formula**: \( PMT = \frac{P\left(\frac{p}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-nt}\right]} \) becomes: \( PMT = \frac{91,200 \times 0.0083333}{1 - (1 + 0.0083333)^{-360}} \) After calculations, you will find that the monthly payment is approximately **$799** when rounded to the nearest dollar. So, in summary, the regular monthly payment, excluding taxes and insurance, is roughly **$799**!