A home is purchased for $420,000 with a 6% down payment. Find the monthly payment for a 30-year mortgage at 7.5% interest.

To calculate the monthly payment for the mortgage, we need to follow these steps:

1. Calculate the down payment: 6% of $420,000 2. Subtract the down payment from the home price to find the loan amount 3. Calculate the monthly interest rate by dividing the annual interest rate by 12 4. Use the loan amount, monthly interest rate, and the number of payments (30 years x 12 months) to calculate the monthly payment using the loan amortization formula

Step 1: Calculate the down payment Down payment = home price x down payment percentage = $420,000 x 0.06 = $25,200

Step 2: Find the loan amount Loan amount = home price - down payment = $420,000 - $25,200 = $394,800

Step 3: Calculate the monthly interest rate Monthly interest rate = annual interest rate / 12 = 7.5% / 12 = 0.0075 (in decimal form)

Step 4: Calculate the number of payments Number of payments (N) = number of years x 12 = 30 x 12 = 360 payments

Step 5: Use the loan amortization formula The monthly payment (M) is calculated using the following formula: M = P [i(1+i)^N] / [(1+i)^N – 1] where P is the loan amount, i is the monthly interest rate, and N is the number of payments.

Substitute the values we have: M = $394,800 [0.0075(1+0.0075)^360] / [(1+0.0075)^360 – 1]

Perform the calculations within the brackets and exponents first, and finally the division to find the monthly payment M.

Using a calculator, or a software with financial functions, the exact monthly payment can be calculated. Without the exact calculation, the monthly payment is typically several thousand dollars for a loan like this.

Please note that these calculations do not include other costs related to home purchases such as property taxes, home insurance, and possibly private mortgage insurance (PMI) if the down payment is less than 20%.