Question

While buying a new car, Brett made a down payment of \( \$ 1,000 \) and agreed to make month-end payments of \( \$ 290 \) for the next 4 years and 6 months. He was charged an interest rate of \( 3 \%

Answer 1

To calculate the total cost of the car, we can use the formula for the future value of an annuity. For Brett's car loan, the total cost will be approximately $22,412.61.

Step-by-step explanation:

To calculate the monthly payments and total cost of the car, we can use the formula for the future value of an annuity:

FV = P * ((1 + r)^n - 1) / r

Where:

• FV is the future value of the annuity (the total cost of the car)
• P is the monthly payment
• r is the monthly interest rate
• n is the total number of months of payments

For Brett's car loan:

• P = $290
• r = 0.03/12 (monthly interest rate = annual interest rate / 12)
• n = 4*12 + 6 (4 years and 6 months converted to months)

Using these values, we can calculate:

FV = $290 * ((1 + 0.03/12)^(4*12 + 6) - 1) / (0.03/12)

FV ≈ $22,412.61

So, the total cost of the car will be approximately $22,412.61.