Question

You've decided to buy a house that is valued at $1 million. You have $250,000 to use as a down payment on the house, and want to take out a mortgage for the remainder of the purchase price. Your bank has approved your $750,000 mortgage, and is offering a standard 30 -year mortgage at a 10% fixed nominal interest rate (called the loan's annual percentage rate or APR). Under this loan proposal, your mortgage payment will be per month. (Note: Round the final value of any interest rate used to four decimal places.) Your friends suggest that you take a 15-year mortgage, because a 30 -year mortgage is too long and you will pay a lot of money on interest. If your bank approves a 15-year, $750,000 loan at a fixed nominal interest rate of 10% (APR), then the difference in the monthly payment of the 15 -year mortgage and 30 -year mortgage will be ?(Note: Round the final value of any interest rate used to four decimal places.) It is likely that you won't like the prospect of paying more money each month, but if you do take out a 15-year mortgage, you will make far fewer payments and will pay a lot less in interest. How much more total interest will you pay over

Answer 1

To calculate the monthly mortgage payment for a 30-year and 15-year mortgage, use the formula (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate) ^ (-Number of Months)). The difference in the monthly payment between a 15-year and 30-year mortgage is $1,180.97. Although the monthly payment is higher for the 15-year mortgage, the total interest paid over the life of the loan will be significantly lower compared to the 30-year mortgage.

Step-by-step explanation:

To calculate the monthly mortgage payment for a 30-year mortgage, we can use the formula:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate) ^ (-Number of Months))

Using the given information, the loan amount is $750,000, the annual interest rate is 10% (APR), and the loan term is 30 years. The monthly interest rate can be calculated by dividing the annual interest rate by 12. Substituting these values into the formula, we can calculate the monthly payment to be $6,610.51.

To calculate the monthly mortgage payment for a 15-year mortgage, we can use the same formula. Using the given information, the loan amount is $750,000, the annual interest rate is 10% (APR), and the loan term is 15 years. Substituting these values into the formula, we can calculate the monthly payment to be $7,791.48.

The difference in the monthly payment between the 15-year and 30-year mortgage is $1,180.97. Although the monthly payment is higher for the 15-year mortgage, the total interest paid over the life of the loan will be significantly lower compared to the 30-year mortgage.