The owner of an automobile repair center purchased new electronic diagnostic equipment for $12,000. He paid down and then paid 60 monthly payments of $242.81. Determine the APR of the loan to the nearest one-half of a percent.
Ms Sue has 2 typos in that she used 6 years instead of 5, and 242.81*60 = 14568.86
Her rate would have been
R = 2568.60/(12000*5) = .043 or appr 4.3%
Using compound interest, since the time > 1 year
let the real monthly rate be x
242.81(1 - (1+x)^-60)/x = 12000
1 - (1+x)^-60 = 49.421x
this type of equation is very messy to solve, so let's go to Wolfram
https://www.wolframalpha.com/input/?i=solve+1+-+(1%2Bx)%5E-60+%3D+49.421x
and it said: x = .00659335
or per year : 12(.00659335) = .07912 or appr 7.9%
I sure messed up! Thank you, Reiny!!
To determine the APR (Annual Percentage Rate) of the loan, you need to calculate the interest paid over the loan term and compare it to the principal amount.
First, let's calculate the total amount paid on the loan:
Total amount paid = Down payment + Monthly payments × Number of payments
Down payment = $12,000 (the purchase of the diagnostic equipment)
Number of payments = 60 (as mentioned)
Monthly payments = $242.81 (as mentioned)
Down payment = $12,000
Monthly payments = $242.81 × 60 = $14,568.60 (total monthly payments over the loan term)
Total amount paid = $12,000 + $14,568.60 = $26,568.60
Now, let's calculate the interest paid:
Interest paid = Total amount paid - Principal amount
Principal amount = Down payment = $12,000
Interest paid = $26,568.60 - $12,000 = $14,568.60
To calculate the APR, we need to determine the average annual interest paid over the loan term. Divide the interest paid by the principal amount and multiply by 100 to get a percentage:
APR = (Interest paid / Principal amount) × 100
APR = ($14,568.60 / $12,000) × 100 = 121.405
The APR, rounded to the nearest one-half of a percent, is 121.5%.
60 * 242.81 = 17.568.60
17,568.60 - 12,000 = 5,568.60
I = PRT
5,568.60 = 12,000 * r * 6
5,568.6/72,000 = r