Question

While buying a new car, Mary made a down payment of $1,200 and agreed to make month-end payments of $300 for the next 4 years and 6 months. He was charged an interest rate of 1% compounded semi-annually for the entire term. a. What was the purchase price of the car? Round to the nearest cent b. What was the total amount of interest paid over the term? Round to the nearest cent

Answer 1

a. The purchase price of the car, considering a 1% interest rate compounded semi-annually, is approximately $13,778.29.
b. The total interest paid over the term amounts to $15,000.

a. Purchase Price Calculation:

`\[ \text{Monthly Interest Rate} = (1\%)/(12) = 0.00833333 \]`

`\[ \text{Number of Payments} = (4 \text{ years} + (6)/(12) \text{ years}) * 12 \text{ payments per year} = 54 \]`

`\[ \text{Present Value} = (300 * \left(1 - (1 + 0.00833333)^(-54)\right))/(0.00833333) \]`

`\[ \text{Purchase Price} = \text{Present Value} + 1200 \]`

The calculated purchase price is approximately $13,778.29.

b. Total Interest Paid Calculation:

`\[ \text{Total Payments} = 300 * 54 = 16,200 \]`

`\[ \text{Total Interest Paid} = \text{Total Payments} - \text{Down Payment} \]`

The calculated total interest paid is $15,000.

Therefore, the purchase price of the car is approximately $13,778.29, and the total amount of interest paid over the term is $15,000.