Final answer:
The APR of Lucky Louie's loan is calculated by adding the total cost of the loan, which includes interest and additional fees, and then dividing by the amount financed. The result is multiplied by 365 days and multiplied by 100 to get a percentage. The APR for Louie's loan is 21.05%.
Step-by-step explanation:
To calculate the Annual Percentage Rate (APR) for Lucky Louie's loan, we need to consider all costs associated with the loan, not just the interest charges. The total cost of the loan includes the interest due at payoff, as well as any additional fees that are charged. In this case, Louie is being charged an application fee, a credit check fee, and a processing fee alongside the interest on the loan.
We start by adding all charges together to find the total cost of borrowing:
- Interest: $750
- Application fee: $100
- Credit check fee: $75
- Processing fee: $75
The total cost of the loan is $750 (interest) + $100 (application fee) + $75 (credit check) + $75 (processing fee) = $1,000.
The amount Louie actually receives after the fees are deducted is $5,000 - $250 (total fees excluding interest) = $4,750.
To calculate the APR, we can use the formula APR = (Interest + Fees) / Amount Financed / Loan Period x 365 x 100:
APR = ($750 + $250) / $4,750 / 1 x 365 x 100 = 21.05%
Hence, the APR of Louie's loan is 21.05%, factoring in not only the interest due at payoff but also the combined fees associated with borrowing.