Final answer:
The Effective Annual Rate (EAR) of a payday loan where $1200 is repaid in 2 weeks for a $1000 loan can be calculated using the formula EAR = (1 + i)^n - 1. Here, i is 20%, and with 26 two-week periods in a year, the EAR is found to be significantly high, demonstrating the high cost of such loans.
Step-by-step explanation:
To calculate the Effective Annual Rate (EAR) of a payday loan wherein you agree to repay $1200 in 2 weeks for a $1000 loan, knowing that there are 52 weeks in a year, we'll first determine the interest for one period. In this case, the interest payment is $200 ($1200 repayment - $1000 loan). Since the loan is for 2 weeks, we would have 52/2 = 26 such periods in a year. The EAR can be calculated using the formula: EAR = (1 + i)^n - 1, where i is the periodic interest rate and n is the number of periods per year.
First, we find i by dividing the interest payment by the loan amount (i = $200/$1000 = 0.2 or 20%). Now using the EAR formula: EAR = (1 + 0.2)^26 - 1. Calculating this gives us a tremendously high EAR, indicating the costliness of payday loans.