Alfred Juarez paid off a 15,000 car lon over3 years with monthly payments of $ 487.54 each. Find the finance charge and the APR

487.54 * 36 = 17,551.44

17,551.44 - 15,000 = 2,551.44 interest

2,551.44 / 3 = 850.48

850.48 / 15,000 = 0.0566986 = 5.67% APR

Ms Sue, this has to be done with compound interest

15000 = 487.54( (1+i)^-36)/i

tough to solve ...
I ran it through the Wolfram equation solver and got
i = .00875 per month
so the annual rate is 12(.00875) = .105 = 10.5%

check:
if rate is 10.5%
then i = .105/12 = .00875

PV = 487.54 (1 - 1.00875^-36)/.00875
= 15000.10 , not bad

To find the finance charge and the APR (Annual Percentage Rate) for the car loan, we can use the formula:

Finance Charge = Total Payments - Principal Amount

APR = (Finance Charge / Principal Amount) * (12 / Loan Term in months)

Let's calculate the values:

1. Total Payments:
Since Alfred made monthly payments of $487.54 each for 3 years, the total number of payments is:

3 years * 12 months/year = 36 payments

Hence, the total payments made by Alfred are:

Total Payments = Monthly Payment * Number of Payments
Total Payments = $487.54 * 36
Total Payments = $17,551.44

2. Principal Amount:
The principal amount is the original loan amount borrowed, which in this case is $15,000.

Principal Amount = $15,000

3. Finance Charge:
The finance charge can be calculated using the formula mentioned earlier:

Finance Charge = Total Payments - Principal Amount
Finance Charge = $17,551.44 - $15,000
Finance Charge = $2,551.44

Therefore, the finance charge for the car loan is $2,551.44.

4. APR:
The APR (Annual Percentage Rate) can be calculated using the formula mentioned earlier:

APR = (Finance Charge / Principal Amount) * (12 / Loan Term in months)
APR = ($2,551.44 / $15,000) * (12 / 36)
APR = 0.170096 * 0.3333
APR = 0.0567

Convert the decimal to a percentage:

APR = 0.0567 * 100
APR ≈ 5.67%

Therefore, the APR for the car loan is approximately 5.67%.

Note: It's important to consider that the calculated APR may slightly differ from the actual APR due to rounding errors or other factors. It's always best to consult the lender for the precise APR.