Final answer:
a.) The monthly payments for a $375,000 home with a 30-year mortgage at 4.74% interest and a 30% down payment are $1,371.49. b.) The total amount paid for principal and interest over 30 years is $493,616.40. c.) Financing the home for 15 years instead of 30 years saves $129,541.40.
Step-by-step explanation:
a.) Monthly Payments:
To calculate the monthly payments, we need to determine the loan amount and the interest rate. Since the home costs $375,000 and you're putting down 30% as a down payment, the loan amount is $375,000 - (0.3 * $375,000) = $262,500.
We can use the formula for calculating the monthly payment of a mortgage: M = P * (r(1 + r)^n) / ((1 + r)^n - 1), where M is the monthly payment, P is the loan amount, r is the monthly interest rate (4.74%/12 = 0.00395), and n is the total number of payments (30 years * 12 months/year = 360 months).
Plugging in the values, we get: M = $262,500 * (0.00395(1 + 0.00395)^360) / ((1 + 0.00395)^360 - 1) = $1,371.49 (rounded to the nearest cent).
b.) Total Amount Paid:
To calculate the total amount paid for principal and interest, we need to multiply the monthly payment by the total number of payments (360 months). Total amount paid = $1,371.49 * 360 = $493,616.40.
c.) Amount Saved with 15-year Financing:
To calculate the amount saved if the home is financed for 15 years instead of 30 years, we need to calculate the total amount paid for principal and interest for a 15-year mortgage. We can use the same formula as in part b, but with a total number of payments of 15 years * 12 months/year = 180 months. Plugging in the values, we get: M = $262,500 * (0.00395(1 + 0.00395)^180) / ((1 + 0.00395)^180 - 1) = $2,022.65 (rounded to the nearest cent). Total amount paid = $2,022.65 * 180 = $364,075.00.
The amount saved is the difference between the total amount paid for 30-year financing and 15-year financing: $493,616.40 - $364,075.00 = $129,541.40.