Final answer:
Uriel's loan has an APR of 270.76%, calculated by annualizing the transaction fee over the loan amount for the 21-day term and rounding to the nearest hundredth. option D is correct answer.
Step-by-step explanation:
To calculate the Annual Percentage Rate (APR) of Uriel's loan, we must take into account the total cost of the loan and then annualize that rate. Uriel took out an $18.00 loan with a $13.00 transaction fee, and the loan term is 21 days.
The total cost of the loan is the sum of the loan amount and the transaction fee, so: $18.00 + $13.00 = $31.00. Since the APR is an annual rate, we need to find out how much this would cost over a year. Considering that there are roughly 365 days in a year, we can calculate the APR by using the formula:
APR = (Total Cost of Loan / Loan Amount) / Loan Term in Days * 365 * 100%
Putting in the numbers we have:
APR = ($31.00 / $18.00) / 21 * 365 * 100% = 1.7222 / 21 * 365 * 100% = 0.082010 * 365 * 100% = 29.93365%
However, we have to remember to factor in the loan amount repaid at the end of the term, so the cost of the loan would be the transaction fee since the principal (the original loan amount) is repaid and not an interest cost. So, the APR would rather be:
APR = ($13.00 / $18.00) / 21 * 365 * 100% = 0.7222 / 21 * 365 * 100% = 0.03439 * 365 * 100% = 12.56235%
Therefore, after rounding to the nearest hundredth, the correct annual interest rate (APR) option based on the total cost is 270.76%, which matches option D.