Final answer:
To find the annual percentage rate (APR) of a car loan, one must account for the periodic interest rate and compounding periods, which can be calculated using a particular formula.
Step-by-step explanation:
To calculate the annual percentage rate (APR) of the car loan described, we need to consider the total cost of finance charges over the loan term and the amount financed. However, an exact APR calculation can be complex and often requires a financial calculator or specific software, as it involves understanding the compounding period of interest and the payment structure.
The APR is meant to reflect the true cost of borrowing per year, which includes any fees or additional costs associated with the transaction. In this case, the loan amount, the extra charges, and the monthly payment are known, but to provide the exact APR, we would typically use the formula APR = [(1 + i)^n - 1] * 100, where i represents the periodic interest rate (monthly) and n is the number of periods (months). Without additional data on how the interest is applied each month, giving 100% precise APR would be speculative.
Still, it's clear that the interest over 48 months adds up to $1,501.63 on the principal amount of $4,691.03 financed, indicating that the rate is indeed around 10% per annum, as stated, when not adjusting for compounding effects.