To determine the annual percentage rate (APR) for the tax refund anticipation loan, we need to use the given loan amount, total fees paid, and the term of the loan. The formula to calculate APR is as follows:
[tex]\[ \text{APR} = \left( \frac{\text{Total Fees Paid}}{\text{Loan Amount}} \right) \times \left( \frac{365}{\text{Loan Term}} \right) \times 100 \][/tex]
Given:
- Loan Amount = \[tex]$985
- Total Fees Paid = \$[/tex]135
- Loan Term = 10 days
Let's plug in these values into the formula:
1. Calculate the fraction of fees paid relative to the loan amount:
[tex]\[ \frac{135}{985} \][/tex]
2. Multiply this fraction by the number of days in a year (365) and divide by the loan term (10 days):
[tex]\[ \left( \frac{135}{985} \right) \times \left( \frac{365}{10} \right) \][/tex]
3. Convert this to a percentage by multiplying by 100.
First, compute the fraction:
[tex]\[ \frac{135}{985} \approx 0.13706 \][/tex]
Next, multiply by 365/10:
[tex]\[ 0.13706 \times 36.5 \approx 5.0025 \][/tex]
Finally, convert to percentage by multiplying by 100:
[tex]\[ 5.0025 \times 100 \approx 500.25 \][/tex]
Rounding to the nearest percent gives:
[tex]\[ 500\% \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{500\%} \][/tex]
And from the provided options, the best answer is:
d. 500%
