1. **State the problem:** A couple wants to buy a house costing $310,000. The bank requires a 20% down payment. The rest is financed with a 30-year fixed mortgage at 9.5% annual interest, paid monthly. 2. **Find the down payment:** The down payment is 20% of the house price. $$\text{Down payment} = 0.20 \times 310000 = 62000$$ 3. **Find the loan amount (mortgage):** The mortgage is the house price minus the down payment. $$\text{Mortgage} = 310000 - 62000 = 248000$$ 4. **Find the monthly payment:** Use the mortgage payment formula for fixed-rate loans: $$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$ where: - $M$ = monthly payment - $P$ = loan amount = 248000 - $r$ = monthly interest rate = $\frac{9.5\%}{12} = \frac{0.095}{12} \approx 0.0079167$ - $n$ = total number of payments = $30 \times 12 = 360$ Calculate: $$M = 248000 \times \frac{0.0079167(1+0.0079167)^{360}}{(1+0.0079167)^{360} - 1}$$ First, compute $(1+0.0079167)^{360}$: $$ (1.0079167)^{360} \approx 18.349$$ Then: $$M = 248000 \times \frac{0.0079167 \times 18.349}{18.349 - 1} = 248000 \times \frac{0.1452}{17.349} = 248000 \times 0.008367 = 2075.62$$ 5. **Final answers:** - Down payment: $62000$ - Mortgage amount: $248000$ - Monthly payment: $2075.62$