A man borrowed $85,000, to be repaid in monthly installments of $823.76 at 11.5 percent annual interest. How much of his first month's payment was applied to reducing the principal amount of the loan?

A man borrowed $85,000, to be repaid in monthly installments of $823.76 at 11.5 percent annual interest. How much of his first month's payment was applied to reducing the principal amount of the loan?

• A. $9.18
• B. $814.58
• C. $823.76
• D. $815.00

Answer: (A)

When a loan is paid with regular monthly installments, each payment first covers the interest on the outstanding balance, and whatever is left reduces the principal. Here, the monthly interest rate is the annual rate divided by 12: 0.115 / 12 = 0.0095833. Interest on the initial balance of 85,000 is 85,000 × 0.0095833 ≈ 814.58. The payment is 823.76, so the portion that goes toward lowering the principal is 823.76 − 814.58 = 9.18. So, $9.18 of the first payment reduces the loan principal; the rest covers interest.

When a loan is paid with regular monthly installments, each payment first covers the interest on the outstanding balance, and whatever is left reduces the principal. Here, the monthly interest rate is the annual rate divided by 12: 0.115 / 12 = 0.0095833. Interest on the initial balance of 85,000 is 85,000 × 0.0095833 ≈ 814.58. The payment is 823.76, so the portion that goes toward lowering the principal is 823.76 − 814.58 = 9.18. So, $9.18 of the first payment reduces the loan principal; the rest covers interest.