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%
treating it as simple interest at r%, that means
550(15 * (r/100)/365) = 30
r = 132.73%
check:
1.3273 * 15/365 * 550 = 30.00
Oh boy, we're talking about payday loans now? Well, let me put on my clown hat and try to calculate this for you!
If you borrow $550 and pay a fee of $30, we can consider the fee as the interest paid. In 15 days, you are repaying the full amount. So the total amount paid would be $550 + $30 = $580.
Now, we need to figure out the equivalent annual interest rate. Since there are 365 days in a year, we can calculate it by dividing the total interest paid ($30) by the initial loan amount ($550), and then multiplying by the number of days in a year.
(30 / 550) * 365 = 20.9090909...
Rounding to the nearest percent, the equivalent annual interest rate on this payday loan is about 21%. That's one expensive clown show! Remember, friends, payday loans can come back to haunt you like a bad circus act, so try to avoid them if you can!
To find the equivalent annual interest rate, known as the Annual Percentage Rate (APR), we need to determine the total interest paid over a year.
First, let's calculate the interest paid on the loan. The loan amount is $550, and we are charged a $30 fee. Therefore, the interest paid would be $30.
Next, we need to determine the interest paid over a year. Since the loan is for 15 days, we need to calculate how many times this 15-day period fits into a year. There are 365 days in a year.
So the number of 15-day periods in a year is: 365 / 15 = 24.3333...
Now, we multiply the interest paid for 15 days by the number of periods in a year:
Interest paid over a year = $30 * 24.3333... = $729.9999...
Rounding to the nearest dollar, the interest paid over a year is $730.
Finally, we can calculate the equivalent annual interest rate (APR):
APR = (Total interest paid / Loan amount) * 100
APR = ($730 / $550) * 100
APR ≈ 132.73%
Rounding to the nearest percent, the equivalent annual interest rate is approximately 133%.
To calculate the equivalent annual interest rate, you first need to determine the total amount repaid, including the fee. Then you can calculate the interest rate.
Step 1: Find the total amount repaid
To find the total amount repaid, add the loan amount ($550) to the fee ($30):
Total amount repaid = Loan amount + Fee = $550 + $30 = $580
Step 2: Calculate the annual interest rate
Since the loan is for 15 days, you need to annualize the interest rate. To do this, divide the fee by the loan amount and then multiply by the number of times the loan would be made in a year.
Annual interest rate = (Fee / Loan amount) x (365 / Loan term in days)
In this case, the loan term is 15 days, so:
Annual interest rate = (30 / 550) x (365 / 15)
Performing the calculation:
Annual interest rate = (0.0545) x (24.33) = 1.325685
To round the annual interest rate to the nearest percent, you get:
Annual interest rate ≈ 1.33%
Therefore, the equivalent annual interest rate for this payday loan is approximately 1.33%.