1. **State the problem:** Calculate various mortgage-related amounts for a home priced at 237000 with a 20% down payment, three points at closing, and a 30-year fixed-rate mortgage at 7% interest. 2. **Find the required down payment:** The down payment is 20% of the home price. $$\text{Down payment} = 0.20 \times 237000 = 47400$$ 3. **Find the amount of the mortgage:** Mortgage amount is the home price minus the down payment. $$\text{Mortgage} = 237000 - 47400 = 189600$$ 4. **Calculate the cost of three points at closing:** Points are fees based on the mortgage amount. One point = 1% of mortgage. $$\text{Points cost} = 3\% \times 189600 = 0.03 \times 189600 = 5688$$ 5. **Find the monthly payment (PMT):** Use the formula for monthly mortgage payment: $$PMT = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$ where $P = 189600$ (loan amount), $r = \frac{7\%}{12} = \frac{0.07}{12} \approx 0.0058333$ (monthly interest rate), $n = 30 \times 12 = 360$ (total payments). Calculate: $$PMT = 189600 \times \frac{0.0058333(1+0.0058333)^{360}}{(1+0.0058333)^{360} - 1}$$ First compute $(1+0.0058333)^{360} \approx 10.677$. Then: $$PMT = 189600 \times \frac{0.0058333 \times 10.677}{10.677 - 1} = 189600 \times \frac{0.0623}{9.677} = 189600 \times 0.00644 = 1221$$ Rounded to nearest dollar, monthly payment is $1221$. **Final answers:** - Down payment: 47400 - Mortgage amount: 189600 - Points cost: 5688 - Monthly payment: 1221