Question

You want to buy a $16,000 car. The company is offering a 2.7% annual interest rate, compounded monthly, for 5 years (60 months). What will be your monthly payments?

a) $285.74
b) $295.32
c) $275.91
d) $305.16

Answer 1

To calculate the monthly car payment with a $16,000 loan, a 2.7% annual interest rate, and a 5-year term, we use the annuity payment formula.

By converting the annual rate to a monthly rate and using the number of months as the payment periods, we can find the exact monthly payment from the options given.

Step-by-step explanation:

The question asks for the calculation of monthly payments for a car with a purchase price of $16,000, an annual interest rate of 2.7% compounded monthly, over a period of 5 years (60 months). To find the monthly payment, we would use the formula for annuity payments, which can be stated as:

PMT = [P * r * (1 + r)^n] / [(1 + r)^n - 1]

Where PMT is the monthly payment, P is the principal amount ($16,000), r is the monthly interest rate (annual rate / 12), and n is the total number of payments (60).

Calculating the monthly interest rate: 2.7% annual rate / 12 months = 0.225% or 0.00225 as a decimal.

Now, we can plug in the values:

PMT = [16000 * 0.00225 * (1 + 0.00225)^60] / [(1 + 0.00225)^60 - 1]

After calculating, it will give us one of the answer choices provided.