Determine the annual percentage rate (APR) for a tax refund anticipation loan based on the following information. (Round to the nearest percent.)
amount of loan = $985
total fees paid = $135
term of loan = 10 days
A. 50%
B. 137%
C. 266%
D. 500%
Please select the best answer from the choices provided.
Answer (2)
Calculate the simple interest rate: 985 135 ≈ 0.13706 .
Determine the annualization factor: 10 365 = 36.5 .
Calculate the APR: 0.13706 × 36.5 ≈ 5.00279 .
Convert to percentage and round: 5.00279 × 100 ≈ 500% . The final answer is 500% .
Explanation
Understanding the Problem We are asked to determine the annual percentage rate (APR) for a tax refund anticipation loan. We are given the amount of the loan, the total fees paid, and the term of the loan.
Identifying Given Information The amount of the loan (principal) is $985. The total fees paid is $135. The term of the loan is 10 days.
Calculating the APR First, we calculate the interest paid on the loan, which is equal to the total fees paid. I n t eres t = F ees = $135 Next, we calculate the simple interest rate for the term of the loan (10 days). S im pl e I n t eres t R a t e = P r in c i p a l I n t eres t = 985 135 ≈ 0.13706 Then, we annualize the simple interest rate. Since the loan term is 10 days, and there are 365 days in a year, the annualization factor is 10 365 = 36.5 .
Now, we calculate the APR by multiplying the simple interest rate by the annualization factor. A PR = S im pl e I n t eres t R a t e × A nn u a l i z a t i o n F a c t or = 985 135 × 10 365 ≈ 0.13706 × 36.5 ≈ 5.00279 Convert the APR to a percentage by multiplying by 100. A PR ( Finally, we round the APR to the nearest percent, which is 500%.
Selecting the Best Answer Comparing the calculated APR with the given options, we find that the closest one is 500%.
Examples
Understanding APR is crucial when evaluating loans or credit options. For instance, if you're considering a short-term loan to cover immediate expenses, knowing the APR helps you compare the true cost against other options like credit cards or lines of credit. A higher APR indicates a more expensive loan, influencing your decision to seek alternatives or negotiate better terms. This calculation is also applicable in business when assessing the cost-effectiveness of short-term financing for inventory or operational needs.
The annual percentage rate (APR) for the tax refund anticipation loan, based on calculations, is approximately 500%. Therefore, the best answer is D. 500%.
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