Final answer:
The monthly payments on a $12,000 car loan at 3% compounded monthly for 4 years would be approximately $268.37. The total interest paid over the life of the loan would be approximately $2,208.44.
Step-by-step explanation:
To calculate the monthly payments on a car loan, we can use the formula for the present value of an annuity:
Monthly Payment = P * (r(1+r)n) / ((1+r)n - 1)
where P is the principal amount, r is the monthly interest rate, and n is the number of months. For this specific case, the principal amount is $12,000, the monthly interest rate is 3% divided by 100 and divided by 12, and the number of months is 4 years multiplied by 12. Plugging these values into the formula, we get:
Monthly Payment = $12,000 * (0.03/12(1+0.03/12)4*12) / ((1+0.03/12)4*12 - 1)
Calculating this expression gives us a monthly payment of approximately $268.37.
To calculate the amount of interest paid over the life of the loan, we can use the formula for the total interest paid on an annuity:
Total Interest = (Monthly Payment * n) - P
where P is the principal amount and n is the number of months. Plugging in the values, we get:
Total Interest = ($268.37 * 4*12) - $12,000
Calculating this expression gives us a total interest payment of approximately $2,208.44.