A payday loan company charges a $30 fee for a $550 payday loan that will be repaid in 15 days. Treating the fee as interest paid, what is the equivalent annual interest rate?
% interest Round to the nearest percent. This will be over 100%
$30 fee for 15 days is $2 per day
365 days in a year ... $730 per year
(730 / 550) * 100% = ?
To calculate the equivalent annual interest rate, we need to first calculate the total amount repaid on the payday loan.
The loan amount is $550, and there is a $30 fee. Therefore, the total amount repaid on the loan is $550 + $30 = $580.
Next, we need to find the interest paid over a 15-day period. To find the daily interest rate, we divide the fee by the number of days in the loan term:
$30 / 15 days = $2 per day
To calculate the annual interest rate, we multiply the daily interest rate by the number of days in a year (365):
$2 * 365 = $730
The equivalent annual interest rate is $730 over a $550 loan amount. To find the interest rate as a percentage, we divide the interest by the loan amount:
($730 / $550) * 100 = 132.73
Rounding to the nearest percent, the equivalent annual interest rate is approximately 133%.
To calculate the equivalent annual interest rate for a payday loan, we need to consider the fee charged and the duration of the loan. In this case, the loan amount is $550, and the fee charged is $30.
First, let's calculate the total amount that needs to be repaid. The loan amount of $550 plus the fee of $30 gives a total repayment amount of $580.
Next, we need to find the interest paid on the loan. The interest paid can be calculated by subtracting the loan amount from the total repayment amount. In this case, $580 - $550 = $30.
Since the fee is treated as interest paid, we can consider it as the interest amount for the loan. To find the equivalent annual interest rate, we need to calculate the interest rate for a year based on the interest amount of $30.
To calculate the annual interest rate, we can use the following formula:
Annual Interest Rate = (Interest Amount / Loan Amount) * (365 / Days of Loan)
In this case, the interest amount is $30, the loan amount is $550, and the duration of the loan is 15 days.
Annual Interest Rate = (30 / 550) * (365 / 15)
Calculating the above expression gives us:
Annual Interest Rate = 0.0545 * 24.3333
Annual Interest Rate ≈ 1.326 or 132.6% (rounded to the nearest percent)
Therefore, the equivalent annual interest rate for this payday loan is approximately 132.6%, or 133% when rounded to the nearest percent.