Payday lenders are firms that make short-term (often one- to two-week) loans to consumers. The intent is to provide households with some extra cash in advance of the next paycheck. According to the loan terms, if you obtain a two-week loan of $500, in two weeks (i.e., 14 days), you have to repay $565.45.
1. What is your two-week interest charge expressed as a percentage of the loan received? (i.e. your periodic interest rate over the 14-day period)?
2. If the interest is compounded every 14 days, how many compounding periods do you have in one year (assuming 365 days in a year)? Using this number of compounding periods and the periodic rate for the 14-day loan you found in (1), calculate the APR of the payday lenders’ loan.
3. Using the number of compounding periods and the APR that you found in (2), find the Effective Annual Rate (EAR) on this loan. As in (2), interest is compounded every 14 days and there are 365 days in a year.
4. Suppose the payday lender charges the same APR as it does right now for a $500 loan, but changes its compounding frequency to daily. Assuming daily compounding (365 days in a year) and the APR found in 2, what would be the EAR on this loan?