Question

if a 24-day single payment loan has a periodic interest rate of 8.4%, what is the approximate APR of the loan?

20.2%
201.6%
12.8%
127.8%

Answer 1

To calculate the APR (Annual Percentage Rate) for a single payment loan, we first need to convert the periodic interest rate into an annual rate. Given that the periodic interest rate is 8.4% for a 24-day loan, we can find the APR as follows:

1. **Convert the interest rate from a percentage to a decimal**:
\[
\text{Periodic interest rate} = 8.4\% = 0.084
\]

2. **Calculate the number of periods in a year**:
Since the loan is for 24 days, we can find out how many such periods there are in a year.
\[
\text{Days in a year} = 365 \text{ days}
\]
\[
\text{Number of periods in a year} = \frac{365 \text{ days}}{24 \text{ days}} \approx 15.2083
\]

3. **Multiply the periodic interest rate by the number of periods in a year to find the APR**:
\[
\text{APR} = \text{Periodic interest rate} \times \text{Number of periods in a year}
\]
\[
\text{APR} = 0.084 \times 15.2083 \approx 1.27575
\]

4. **Convert the APR to a percentage**:
\[
\text{APR} \approx 1.27575 \times 100 \approx 127.58\%
\]

This rounds to approximately **127.8%**.

Thus, the approximate APR of the loan is **127.8%**.