Final answer:
Dan Carter's loan has an annual interest rate of 9%, obtained by calculating the interest from the total repayment amount and dividing by the principal amount for one year.
Step-by-step explanation:
To calculate the annual interest rate on Dan Carter's loan, we can use the formula for simple interest, which is I = PRT, where I is the interest, P is the principal amount, R is the rate of interest per year, and T is the time in years. We are given that the total amount repaid is $1,635 and the original loan amount (principal) is $1,500. That means the total interest I paid over the loan period is $1,635 - $1,500 = $135.
Assuming the loan is for one year, we would calculate the interest rate as follows:
- I = $135
- P = $1,500
- T = 1 year
We can now solve for R using the simple interest formula:
I = PRT
$135 = $1,500 × R × 1
Dividing both sides by $1,500, we get:
R = $135 / $1,500
R = 0.09
Converting the decimal into a percentage, we multiply by 100:
Annual Interest Rate = R × 100 = 0.09 × 100 = 9%