Calculate Derek's Remaining Mortgage Balance after 96 Payments

What is Derek's remaining mortgage balance after making 96 payments?

Derek borrows $306,097.00 to buy a house. He has a 30-year mortgage with a rate of 4.28%. After making 96 payments, how much does he owe on the mortgage?

Answer:

Currency: Round to: 2 decimal places.

Derek owes $257,107.36 on the mortgage after making 96 payments.

To calculate the remaining balance on the mortgage after 96 payments, we need to consider the loan amount, interest rate, and the number of payments made. The formula to calculate the remaining balance on a mortgage is:

Remaining Balance = Principal × (1 + Monthly Interest Rate) ^ Number of Payments – (Monthly Payment × [((1 + Monthly Interest Rate) ^ Number of Payments) – 1] / Monthly Interest Rate)

Given that Derek borrowed $306,097.00 with a 30-year mortgage and an interest rate of 4.28%, we can calculate the monthly interest rate by dividing the annual interest rate by 12. In this case, the monthly interest rate is 0.0428 / 12 = 0.0035667.

Next, we calculate the monthly payment using the loan amount, interest rate, and the number of payments. For a 30-year mortgage, the number of payments is 30 × 12 = 360. Using a mortgage payment calculator, we find that the monthly payment is $1,500.77.

Now we can substitute these values into the formula to calculate the remaining balance after 96 payments. Plugging in the numbers, we have:

Remaining Balance = $306,097.00 × (1 + 0.0035667) ^ 96 – ($1,500.77 × [((1 + 0.0035667) ^ 96) – 1] / 0.0035667)

After evaluating this expression, we find that Derek owes $257,107.36 on the mortgage after making 96 payments.