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:
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Convert the interest rate from a percentage to a decimal: \[ \text{Periodic interest rate} = 8.4% = 0.084 \]
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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. \[ \text{Days in a year} = 365 \text{ days} \] \[ \text{Number of periods in a year} = \frac{365 \text{ days}}{24 \text{ days}} \approx 15.2083 \]
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Multiply the periodic interest rate by the number of periods in a year to find the APR: \[ \text{APR} = \text{Periodic interest rate} \times \text{Number of periods in a year} \] \[ \text{APR} = 0.084 \times 15.2083 \approx 1.27575 \]
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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%.