Question

While buying a new car, Cynthia made a down payment of $1,100

and agreed to make month-end payments of $340 for the next 4 years
and 7 months. She was charged an interest rate of 4% compounded
semi-an

Answer 1

To find the total cost of the car, we need to calculate the future value of the monthly payments and the down payment. The future value can be calculated using the formula for future value of an ordinary annuity. By plugging in the values, we find that the total cost of the car is $21,725.59.

Step-by-step explanation:

To find the total cost of the car, we need to calculate the future value of the monthly payments and the down payment. We can use the formula for future value of an ordinary annuity to do this:

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

Where FV is the future value, PMT is the monthly payment, r is the interest rate per period, and n is the number of periods. In this case, PMT = $340, r = 0.04/12 (because the interest is compounded semi-annually), and n = 4 years and 7 months (which is 4 * 12 + 7 = 55 months). Plugging these values into the formula, we get:

FV = $340 * ((1 + 0.04/12)^55 - 1) / (0.04/12)

Solving this equation, we find that the future value of the monthly payments is $20,625.59. Adding the down payment of $1,100, the total cost of the car is $21,725.59.