A loan of 4,800 dollars has an APR of 12% with monthly payments over 24 months. What is the total finance charge (total interest paid) on this loan?

Introduction / Context:
This problem combines loan amortization with the concept of a finance charge. The finance charge on an installment loan is the total interest paid over the life of the loan, which is the difference between the sum of all payments and the original principal.

Given Data / Assumptions:

• Loan principal PV = 4,800 dollars.
• APR (annual percentage rate) = 12%.
• Interest is compounded monthly, so monthly rate i = 12% / 12 = 1% = 0.01.
• Number of monthly payments n = 24.
• Payments are equal in amount each month.

Concept / Approach:
First find the fixed monthly payment using the annuity formula:
Payment R = PV * i / (1 - (1 + i)^(-n)) Then find the total of all payments and subtract the principal to get the finance charge:
Finance charge = R * n - PV

Step-by-Step Solution:
Step 1: Set i = 0.01 and n = 24. Step 2: Compute the denominator 1 - (1.01)^(-24). Step 3: Compute the monthly payment R = 4800 * 0.01 / denominator ≈ 225.95 dollars. Step 4: Compute the total of all payments: R * n ≈ 225.95 * 24 ≈ 5,422.86 dollars. Step 5: Finance charge = 5,422.86 - 4,800 ≈ 622.86 dollars. Thus the total interest paid over the life of the loan is about 622.86 dollars.

Verification / Alternative Check:
You can build a month by month amortization table, computing interest each month as 1% of the outstanding balance and subtracting the remainder of the payment from principal. Summing all the interest entries will give a total very close to 622.86 dollars.

Why Other Options Are Wrong:
Option B (522.80 dollars) and option C (322.80 dollars) are too small and would correspond to either a lower APR or a shorter term.
Option D (632.80 dollars) overestimates the finance charge relative to the computed payment.
Option E (422.80 dollars) is also inconsistent with the described loan terms.

Common Pitfalls:
Some learners confuse APR with the monthly rate and use 12% as the monthly rate instead of 1%, which gives absurd results. Others forget that the finance charge is total payments minus principal rather than simply principal times rate times time.

Final Answer:
The total finance charge paid on this loan is approximately 622.86 dollars.