Lane French had a bad credit rating and went to a local cash center. He took out a $103 loan payable in five weeks at $123.
What is the percent of interest paid on this loan? Do not round denominator before dividing. (Use calendar year. Round your answer to 2 decimal places. Omit the "%" sign in your response.)
Percentage of Interest = 201.94 %
Explanation:
$ 123
– 103
___________
$ 20 Interest
P R T
5
103 × ? × ______
52
$20.00
__________ = 201.94% interest paid on loan
9.903846154
To calculate the percentage of interest paid on the loan, we need to find the amount of interest paid and then calculate it as a percentage of the loan amount.
First, let's find the amount of interest paid on the loan. The loan amount is $103, and the total amount repaid is $123. So the interest paid can be calculated by subtracting the loan amount from the total amount repaid:
Interest paid = Total amount repaid - Loan amount
Interest paid = $123 - $103
Interest paid = $20
Now that we have the amount of interest paid, let's calculate the percentage of interest on the loan. Since the loan term is five weeks, it represents a fraction of the year. To convert it to a yearly basis, we need to divide it by the total number of weeks in a year (52 weeks). This will give us the interest rate for a full year.
Interest rate on a yearly basis = Interest paid / Loan amount × (52 weeks / 5 weeks)
Interest rate on a yearly basis = $20 / $103 × (52 weeks / 5 weeks)
Calculating this gives us a decimal value. To convert it to a percentage, we multiply it by 100.
Interest rate as a percentage = (Interest rate on a yearly basis) × 100
Interest rate as a percentage = ((Interest paid / Loan amount) × (52 weeks / 5 weeks)) × 100
Now let's substitute the values and calculate the answer:
Interest rate as a percentage = (($20 / $103) × (52 weeks / 5 weeks)) × 100
Interest rate as a percentage = (0.19417) × 100
Interest rate as a percentage ≈ 19.42
Therefore, the percentage of interest paid on this loan is approximately 19.42%.