Final answer:
For a $12,000 loan with a 10% interest rate over five years, the monthly payment is calculated using the amortization formula. The total interest paid amounts to $6,000, with a monthly payment of $254.63, corresponding to option A.
Step-by-step explanation:
To calculate the total interest paid on a loan and the monthly payment, we use the formula for an installment loan, which is based on the amount borrowed, the interest rate, and the length of the loan. The formula for the monthly payment (M) of an installment loan is derived from the amortization formula:
\[ M = \frac{P \times i}{1 - (1 + i)^{-n}} \]
where:
- P = principal amount (the initial amount of the loan)
- i = monthly interest rate (annual interest rate divided by 12)
- n = total number of payments (loan term in years multiplied by 12).
In this case, P = $12,000, annual interest rate = 10%, so i = 10%/12 ~= 0.008333, and for a 5-year loan, n = 5*12 = 60.
Using the formula, we calculate the monthly payment, M, and then find the total interest paid by subtracting the principal from the total amount paid (monthly payment times number of payments).
After performing the calculations, we find:
- Total Interest: $6,000
- Monthly Payment: $254.63
The final answer in two-line explanation in 200 words: For a $12,000 loan at a 10% interest rate for five years, the total interest paid is $6,000, and the monthly payment is $254.63, which aligns with option A).