Question

You have taken out a 60 -month, $20,000 car loan with an APR of 8%, compounded monthly. The monthly payment on the loan is $405.53. Assume that right after you make your 50 th payment, the balance of the loan is $3,910.49. How much of your next payment goes toward principal and how much goes toward interest? Compare this with the prinicipal and interest paid in the first month's payment.

Answer 1

In the 51st payment of a 60-month, $20,000 car loan at 8% APR compounded monthly, $26.20 goes toward interest and $379.33 towards the principal. Comparatively, in the first month's payment of $405.53, $134 was for interest and $271.53 for the principal. Over time, more of each payment is applied to the principal rather than interest.

Step-by-step explanation:

To determine how much of the 51st payment of $405.53 goes toward the principal and how much goes toward interest, we need to apply the loan amortization process that car loans typically follow, which involves calculating interest on the remaining balance and then applying the rest of the payment to reduce the principal.

To calculate the interest portion of the 51st payment after 50 payments have been made, with a balance of $3,910.49, use the formula for monthly interest: Interest = Remaining balance x (APR / 12). For an APR of 8%, the monthly interest rate is 0.08/12 = 0.0067. Therefore, the interest portion is $3,910.49 x 0.0067 = $26.20. The rest of the payment, $405.53 - $26.20, which equals $379.33, goes toward the principal.

In the first payment of the loan, the full $20,000 principal amount would be applied to calculate interest. Therefore, the interest for the first payment would be $20,000 x 0.0067 = $134. The remainder of the payment, $405.53 - $134 = $271.53, would have gone toward reducing the principal. Thus, as the loan matures, a greater portion of each payment goes towards the principal and less towards interest.