A borrower obtains a $100,000 mortgage loan for 30 years at 7.5 percent interest. If the monthly payments of $699 are credited first to interest and then to principal, what will be the balance of the principal after the borrower makes the first payment?

A borrower obtains a $100,000 mortgage loan for 30 years at 7.5 percent interest. If the monthly payments of $699 are credited first to interest and then to principal, what will be the balance of the principal after the borrower makes the first payment?

• A. $99,926
• B. $99,400
• C. $100,000
• D. $99,000

Answer: (A)

In a mortgage payment, the amount you pay each month first covers interest on the current balance, and the remainder reduces the principal. For the first month, the balance is the full loan amount, so calculate the interest portion using the monthly rate: 7.5% annual divided by 12 months equals 0.625% per month. The interest due is 100,000 × 0.00625 = 625. The payment is 699, so after paying the interest, the amount left to reduce the principal is 699 − 625 = 74. Subtracting that from the original principal gives 100,000 − 74 = 99,926. So the principal balance after the first payment is 99,926. (Options requiring larger principal reductions or no reduction wouldn’t align with the fact that the monthly payment must first cover the interest.)

In a mortgage payment, the amount you pay each month first covers interest on the current balance, and the remainder reduces the principal. For the first month, the balance is the full loan amount, so calculate the interest portion using the monthly rate: 7.5% annual divided by 12 months equals 0.625% per month. The interest due is 100,000 × 0.00625 = 625.

The payment is 699, so after paying the interest, the amount left to reduce the principal is 699 − 625 = 74. Subtracting that from the original principal gives 100,000 − 74 = 99,926.

So the principal balance after the first payment is 99,926. (Options requiring larger principal reductions or no reduction wouldn’t align with the fact that the monthly payment must first cover the interest.)