Answer :
To determine the annual percentage rate (APR) for a tax refund anticipation loan based on the provided information, we need to follow a systematic approach.
1. Identify the given data:
- Loan amount = [tex]$985 - Total fees paid = $[/tex]135
- Term of loan = 10 days
2. Calculate the daily interest rate:
- The daily interest rate is calculated by dividing the total fees by the loan amount.
[tex]\[ \text{Daily Interest Rate} = \frac{\text{Total Fees}}{\text{Loan Amount}} = \frac{135}{985} \approx 0.1371 \][/tex]
3. Convert the daily interest rate to an annual percentage rate (APR):
- The APR is determined by multiplying the daily interest rate by the number of days in a year (365) and then converting it to a percentage.
[tex]\[ \text{APR} = \text{Daily Interest Rate} \times 365 \times 100 \][/tex]
- Substituting the daily interest rate we found:
[tex]\[ \text{APR} = 0.1371 \times 365 \times 100 \approx 5002.54 \][/tex]
4. Round the APR to the nearest percent:
- The APR of 5002.54 is rounded to the nearest whole number.
[tex]\[ \text{APR Rounded} = 5003\% \][/tex]
5. Determine the correct answer among the provided options:
- The given options are:
a. 50%
b. 137%
c. 266%
d. 500%
- Comparing 5003% to the given options, none of them match exactly. Hence, none of the provided options are correct based on this calculation.
Given this detailed step-by-step solution, the best answer from the choices provided is:
[tex]\[ \text{None of the options given accurately reflect the calculated APR of 5003%.} \][/tex]
1. Identify the given data:
- Loan amount = [tex]$985 - Total fees paid = $[/tex]135
- Term of loan = 10 days
2. Calculate the daily interest rate:
- The daily interest rate is calculated by dividing the total fees by the loan amount.
[tex]\[ \text{Daily Interest Rate} = \frac{\text{Total Fees}}{\text{Loan Amount}} = \frac{135}{985} \approx 0.1371 \][/tex]
3. Convert the daily interest rate to an annual percentage rate (APR):
- The APR is determined by multiplying the daily interest rate by the number of days in a year (365) and then converting it to a percentage.
[tex]\[ \text{APR} = \text{Daily Interest Rate} \times 365 \times 100 \][/tex]
- Substituting the daily interest rate we found:
[tex]\[ \text{APR} = 0.1371 \times 365 \times 100 \approx 5002.54 \][/tex]
4. Round the APR to the nearest percent:
- The APR of 5002.54 is rounded to the nearest whole number.
[tex]\[ \text{APR Rounded} = 5003\% \][/tex]
5. Determine the correct answer among the provided options:
- The given options are:
a. 50%
b. 137%
c. 266%
d. 500%
- Comparing 5003% to the given options, none of them match exactly. Hence, none of the provided options are correct based on this calculation.
Given this detailed step-by-step solution, the best answer from the choices provided is:
[tex]\[ \text{None of the options given accurately reflect the calculated APR of 5003%.} \][/tex]
