1. Payday loans are small, short-term loans that help the borrower get by until his or her next paycheck. Such loans are coming under increasing government scrutiny in many states. According to the Center for Responsible Lending: "Payday loans are small cash advances, usually of $500 or less. To get a loan, a borrower gives a payday lender a postdated personal check or an authorization for automatic withdrawal from the borrower's bank account. In return, he receives cash, minus the lender's fees. For example, with a $300 payday loan, a consumer might pay $50 in fees and get $250 in cash. The lender holds the check or electronic debit authorization for a week or two (usually until the borrower's next payday). At that time, the borrower has the option of (1) paying back the $300 in exchange for the original check, (2) letting the lender deposit the check for $300, or (3) renewing or rolling over the loan, if he is unable to repay it." If a loan amount of $250 is received at t=0, and is repaid with a single payment of $300 at t=2 weeks, what is the interest rate for the single two-week compounding period? (This is the periodic interest rate.) Include a cash flow diagram in your written work.
2. For the payday loan problem, if the borrower is unable to pay off the loan until t = 8 weeks, how much would be owed? (Assume that the periodic interest rate is the value you computed previously.)
3. For the payday loan problem, what is the effective annual interest rate?Don't be shocked -- the answer is big.(Assume that the periodic interest rate is the value you computed previously.)