To determine the annual percentage rate (APR) for the tax refund anticipation loan, follow these steps:
1. Identify the given values:
- Amount of loan: [tex]$985
- Total fees paid: $[/tex]135
- Term of loan: 10 days
2. Calculate the daily interest rate:
The daily interest rate can be found by dividing the total fees paid by the amount of the loan and then dividing by the term of the loan (in days).
[tex]\[
\text{Daily interest rate} = \frac{\text{Total fees paid}}{\text{Amount of loan}} \div \text{Term of loan}
\][/tex]
Substituting the given values:
[tex]\[
\text{Daily interest rate} = \frac{135}{985} \div 10 \approx 0.013705583756345178
\][/tex]
3. Convert the daily interest rate to an annual interest rate:
Since there are 365 days in a year, you multiply the daily interest rate by 365 to convert it to an annual rate.
[tex]\[
\text{Annual interest rate (APR)} = \text{Daily interest rate} \times 365
\][/tex]
Substituting the calculated daily interest rate:
[tex]\[
\text{Annual interest rate (APR)} = 0.013705583756345178 \times 365 \approx 500.25380710659897
\][/tex]
4. Round the APR to the nearest percent:
The APR calculated above is approximately 500.25380710659897%. When rounding to the nearest percent:
[tex]\[
\text{Rounded APR} \approx 500\%
\][/tex]
5. Select the best answer from the given choices:
Upon reviewing the choices, the correctly rounded APR is:
- a. 50%
- b. 137%
- c. 266%
- d. 500%
The nearest percent, 500%, matches choice d. Thus, the best answer is d. 500%.
Therefore, the correct choice is:
D: 500%
