- Identify the principal \(P = \$985\), fees \(I = \$135\), and term \(T = 10\) days.
- Apply the APR formula \(\text{APR} = (\frac{I}{P}) \times (\frac{365}{T})\).
- Perform the calculation: \((\frac{135}{985}) \times 36.5 \approx 5.0025\).
- Convert to a percentage and round to the nearest whole number to get \(\boxed{500\%}\).
Explanation
- Problem Analysis and Formula Identification
To determine the Annual Percentage Rate (APR) for the given tax refund anticipation loan, we identify the following provided values:
- Principal (\(P\)) = \(\$985\)
- Total fees paid (\(I\)) = \(\$135\)
- Loan term (\(T\)) = \(10\) days
The standard formula for calculating the APR is:
\[\text{APR} = \left(\frac{I}{P}\right) \times \left(\frac{365}{T}\right)\]
This formula represents the interest rate if the loan were held for a full year of 365 days.
- Calculation of APR
Now we substitute the identified values into the APR formula:
\[\text{APR} = \left(\frac{135}{985}\right) \times \left(\frac{365}{10}\right)\]
First, we calculate the ratio \(\frac{135}{985} \approx 0.137056\).
Next, we calculate the ratio \(\frac{365}{10} = 36.5\).
Multiplying these two results gives:
\[\text{APR} = 0.137056 \times 36.5 \approx 5.002538\]
To express this as a percentage, we multiply by \(100\%\):
\[\text{APR} \approx 5.002538 \times 100\% = 500.2538\%\]
- Conclusion and Final Selection
Rounding our result to the nearest percent, we obtain \(500\%\). Comparing this with the provided options:
A\(50\%\)
B\(137\%\)
C\(266\%\)
D\(500\%\)
The calculated APR corresponds to option d. Therefore, the correct annual percentage rate is \(\boxed{500\%}\).
Examples
Understanding how to calculate an Annual Percentage Rate (APR) is crucial when dealing with short-term loans, such as payday loans or tax anticipation loans. These loans often carry high fees relative to their short duration, which can lead to surprisingly high APR values when calculated over a standard 365-day year. By mastering this calculation, consumers can better evaluate the true cost of borrowing and make more informed financial decisions, ensuring they are aware of the impact that short-term interest charges have on their total financial health.