Final answer:
The correct option is b). To calculate the monthly payment required to pay off a $20,000 car loan at 6% annual interest, compounded monthly over five years, we use the amortizing loan formula. The monthly payment comes out to be approximately $387, so the closest answer choice is $400 (option b).
Step-by-step explanation:
The question asks for the calculation of the monthly payment to pay off a car loan, with a principal balance of $20,000 after a $5,000 down payment, at a 6% annual interest rate, compounded monthly for five years. To find the monthly payment, we use the formula for an amortizing loan which incorporates the principal amount, the monthly interest rate, and the number of monthly payments.
To calculate the monthly payment, first, we need to identify the key terms: the loan amount (P), which is $25,000 - $5,000 = $20,000, the monthly interest rate (r), which is 6% annually or 0.06 divided by 12, equaling 0.005 per month, and the total number of payments (n), which is 5 years times 12 months per year, equaling 60 payments.
The monthly payment (M) can be calculated using the formula:
M = P[r(1+r)^n] / [(1+r)^n - 1]. Plugging in the values, we get:
M = $20,000[0.005(1+0.005)^60] / [(1+0.005)^60 - 1].
M = $386.66, which is approximately $387 when rounded to the nearest dollar.
So, the nearest value of the required monthly payment to pay off the loan is $400 (option b).