Question

kimberly took out a payday loan for $1500 due in 4 weeks that charged a $135 fee. what is the periodic interest rate of the loan?

A. 9%
B. 36%
C. 117%
D. 468%

Answer 1

To find the periodic interest rate of the loan, we can use the formula:

\[
\text{Interest Rate} = \frac{\text{Fee}}{\text{Principal}} \times 100
\]

In this case, the principal is $1500 and the fee is $135.

1. Calculate the ratio of the fee to the principal:
\[
\frac{135}{1500} = 0.09
\]

2. Convert this to a percentage:
\[
0.09 \times 100 = 9\%
\]

Since the loan is due in 4 weeks, we can calculate the annualized interest rate. To find the annual interest rate, we multiply the periodic interest rate by the number of periods in a year. There are approximately 13 periods in a year (since there are 52 weeks in a year, \(52 / 4 = 13\)).

3. Calculate the annual interest rate:
\[
\text{Annual Interest Rate} = 9\% \times 13 = 117\%
\]

So, the periodic interest rate for the loan is:

**A. 9%** (for the 4-week period)
**C. 117%** (when annualized)

For the question about the periodic interest rate, the answer is A.
If they were asking for the annualized rate, the answer would be C.