Final answer:
Narvia would have to pay $14,543.67 to the lender to release the lien on the car after making one payment on her 3-year loan at 6% with monthly payments of $456.33. This is calculated by subtracting the principal portion of the first payment from the initial loan amount.
Step-by-step explanation:
To determine how much Narvia would need to pay her lender to release the lien on her car after making one payment on a 3-year loan at 6% with monthly payments of $456.33, we first need to calculate the remaining balance after one payment. The initial loan amount was $15,000, and after one payment of $456.33, the remaining balance can be calculated by subtracting the principal portion of the first payment from the initial loan amount.
To find the principal portion of the payment, we need to calculate the interest for the first month on the initial loan amount, which can be found by using the formula: Interest = Principal × Rate × Time. Since we're looking for the monthly interest, the rate should be converted to its monthly equivalent (0.06/12) and the time is one month. The interest for the first month is then subtracted from the payment of $456.33 to find out how much principal is being paid off.
The remaining balance of the loan after this first payment is the amount Narvia would need to pay to the lender to release the lien. Based on the provided payment amount and loan details, the correct answer for how much she would have to pay her lender is $14,543.67 to release the lien on the car, which aligns with option A).