Questions: A couple plans to purchase a house. The bank requires a 10% down payment on the 330,000 house. The couple will finance the rest with a mortgage at 3% annual interest rate with monthly payments over 30 years. Complete the parts below. Do not round any intermediate computations. Round your final answers to the nearest cent if necessary. (a) Find the required down payment. (b) Find the amount of the mortgage. (c) Find the monthly payment.

Solution Steps

The required down payment is calculated as follows: \[ \text{Down Payment} = 0.10 \times 330000 = 33000.0 \]

The mortgage amount is determined by subtracting the down payment from the total house price: \[ \text{Mortgage Amount} = 330000 - 33000 = 297000.0 \]

The monthly payment for the mortgage can be calculated using the formula: \[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} \] where:

• \( P = 297000 \) (mortgage amount)
• \( r = \frac{0.03}{12} = 0.0025 \) (monthly interest rate)
• \( n = 30 \times 12 = 360 \) (total number of payments)

Substituting the values: \[ M = 297000 \frac{0.0025(1 + 0.0025)^{360}}{(1 + 0.0025)^{360} - 1} \approx 1252.1640 \]

Final Answer