Final answer:
To calculate the equivalent simple annual interest rate for a $500 loan with a $15 fee, apply the simple interest formula to find the monthly rate and then multiply by 12 to annualize. The calculation yields an annual rate of 4.32%.
Step-by-step explanation:
To find the equivalent simple annual interest rate for a $500 payday loan with a fee of $15, we use the formula for simple interest:
Interest = Principal × rate × time
In this case, we have:
- Interest = $15 (the fee for borrowing $500)
- Principal = $500
- Time = 1 month (or 1/12 of a year)
Substituting these into the formula and solving for the rate gives us:
$15 = $500 × rate × (1/12)
Dividing both sides by $500 and then by 1/12, we find:
rate = ($15 / $500) × 12
Calculating this yields the monthly interest rate:
rate = 0.03 × 12 = 0.36
To find the annual interest rate, we simply multiply the monthly rate by 12 (since there are 12 months in a year):
Annual interest rate = 0.36 × 12 = 4.32%
Therefore, the equivalent simple annual interest rate for the loan is 4.32%