Final answer:
To determine the total interest saved by choosing a 15-year mortgage over a 30-year one, you calculate the total amount paid for each term, subtract the loan amount, and compare the total interest paid. The 15-year mortgage will have higher monthly payments, but significantly less total interest paid over the life of the loan.
Step-by-step explanation:
To calculate how much total interest one will save by choosing a 15-year mortgage over a 30-year mortgage, we need to determine the interest paid over the life of each loan. We start by identifying the loan amount, which is the price of the house ($750,000) minus the down payment ($120,000), resulting in a loan of $630,000. Using a fixed nominal interest rate of 6% compounded monthly, we can calculate the monthly payment for each mortgage term and then calculate the total interest paid.
The monthly payment for a 15-year mortgage can be found using the formula for an amortizing loan which takes into account the principal amount, the interest rate, and the number of payments. Similarly, we calculate the monthly payment for the 30-year mortgage. After finding the monthly payments, we multiply each by the total number of payments to find the total amount paid for each term. Subtracting the initial loan amount from these totals gives us the total interest paid for each mortgage.
To find the total interest saved by opting for the 15-year mortgage over the 30-year mortgage, subtract the total interest paid on the 15-year mortgage from the total interest paid on the 30-year mortgage. This will show the savings in interest by paying off the loan in a shorter time period, even though the monthly payments will be higher for a 15-year mortgage.