Question

Sam has saved $6500 to purchase his first car. He finds a car that costs $23,500 that he has decided to purchase. The bank said that due to a limited credit history Sam must be able to make a down payment of 25%. Sam decides to pay for the car over a 3-year period. The bank is charging simple interest at 4% per year. How much will Sam pay in interest over the three years that he makes payments, assuming he is making the 25% down payment?

a) $3,000
b) $3,500
c) $4,000
d) $4,500

Answer 1

After calculating a 25% down payment on the car and the remaining amount to be financed, and using the simple interest formula, we determine that Sam will pay $2,115 in interest over three years, which doesn't match any of the provided answer options.

Step-by-step explanation:

First, we must calculate the down payment Sam needs to make on the $23,500 car. A 25% down payment would be $23,500 × 0.25 = $5,875. Since Sam has $6,500 saved, he can afford this down payment.

Next, we subtract the down payment from the total cost of the car to find the amount Sam will need to finance: $23,500 - $5,875 = $17,625. This is the principal amount on which Sam will be charged simple interest at a rate of 4% per year.

To find the total interest paid over 3 years, we use the formula for simple interest: I = P × r × t, where I is interest, P is principal, r is the annual interest rate, and t is the time in years. Therefore, the interest Sam will pay is $17,625 × 0.04 × 3 = $2,115.

Since none of the options provided (a $3,000, b $3,500, c $4,000, d $4,500) match the calculated interest of $2,115, there seems to be an error with the options presented. The correct amount of interest Sam will pay over the three years, based on the calculations provided, is actually $2,115.