Final answer:
The APR for a payday loan with a 10% interest rate for a 2-week period is calculated by multiplying the two-week interest rate by the number of two-week periods in a year, resulting in a 260% APR.
Step-by-step explanation:
To calculate the Annual Percentage Rate (APR) for a payday loan, we need to consider the interest rate for the period of the loan and then extrapolate that to a yearly rate.
The question states there is a 10% interest rate for a 2-week period. Since there are 52 weeks in a year, the 2-week period accounts for ⅒ (or 1/26th) of a year. Therefore, to find the APR, we would multiply the two-week interest rate by the number of two-week periods in a year:
(10% interest for 2 weeks) × (26 periods in a year) = 260% APR
Thus, the APR for the payday loan is a staggering 260%, significantly higher than typical annual interest rates for other types of borrowing such as credit cards or personal loans.