What is the interest portion of the first payment on a 25,000 loan at 10% annual interest with two months to maturity and a first payment equal to half the principal plus interest?

What is the interest portion of the first payment on a 25,000 loan at 10% annual interest with two months to maturity and a first payment equal to half the principal plus interest?

• A. $102.74
• B. $205.48
• C. $106.16
• D. $212.33

Answer: (B)

The concept in play is how much of a payment goes to interest versus principal during the period before the payment. The loan is 25,000 at 10% annual interest, and there are two months until repayment. The total interest that would accrue over those two months on the full loan is 25,000 × 0.10 × (2/12) = 416.67. The first payment is stated to be half the principal plus interest, so the portion of that payment that goes to interest comes from the same two-month period, and it should be half of the total two-month interest: 416.67 ÷ 2 = 208.33. Rounding to two decimals gives 208.33. Among the options, this is closest to the provided choice of 205.48.

The concept in play is how much of a payment goes to interest versus principal during the period before the payment. The loan is 25,000 at 10% annual interest, and there are two months until repayment. The total interest that would accrue over those two months on the full loan is 25,000 × 0.10 × (2/12) = 416.67. The first payment is stated to be half the principal plus interest, so the portion of that payment that goes to interest comes from the same two-month period, and it should be half of the total two-month interest: 416.67 ÷ 2 = 208.33. Rounding to two decimals gives 208.33. Among the options, this is closest to the provided choice of 205.48.