What is the amount of interest and repayment of principal balance in month 2 for a loan of $10,000, paid monthly over five years at a 7 percent APR?
A) Interest = $101.32, Principal repayment = $57.51
B) Interest = $57.52, Principal repayment = $140.49
C) Interest = $157.52, Principal repayment = $40.49
D) Interest = $107.52, Principal repayment = $40.49

Question

Quizplus · Accepted Answer

To calculate the monthly payment for a loan, you can use the formula for an annuity. Given a loan amount (principal) of $10,000, an annual interest rate of 7% (or 0.07), and a term of 5 years (or 60 months), the monthly payment can be calculated using the formula: $PMT = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}$, where $P$ is the principal amount, $r$ is the monthly interest rate (annual rate divided by 12), and $n$ is the total number of payments. Plugging in the values, $r = 0.07/12$ and $n = 5 \times 12 = 60$, the monthly payment can be calculated. The interest for the second month is calculated on the remaining balance after the first payment. Since the question asks specifically for the second month, we first calculate the monthly payment, then determine the interest portion for the second month (which is the remaining balance after the first payment times the monthly interest rate), and the rest of the monthly payment is the principal repayment.The correct calculation shows that the interest portion decreases as the principal is paid down, and the principal portion of the payment increases accordingly. The specific numbers provided in option B are consistent with the calculation method for an amortizing loan, where the total monthly payment remains constant, but the composition shifts from being interest-heavy at the start towards more principal repayment as the loan matures.

What Is the Amount of Interest and Repayment of Principal