Sam got a job at the Brick. He immediately finances a car paying $500 every month for 3 years. The interest is 2.25% compounded semi-annually. How much is the interest cost of the financing?

Question

Quizplus · Accepted Answer

The first step is to calculate the total amount paid over 3 years:
$500/month x 12 months/year x 3 years = $18,000

Next, we need to calculate the interest. Since the interest is compounded semi-annually (twice a year), we need to first calculate the semi-annual interest rate:

2.25% / 2 = 1.125%

Then, we need to calculate the number of periods (in this case, semi-annual periods) over the 3-year term:

3 years x 2 = 6 semi-annual periods

Now we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the total amount paid
P = the principal (in this case, $18,000)
r = the interest rate per period (in this case, 1.125%)
n = the number of times the interest is compounded per period (in this case, 2)
t = the number of periods (in this case, 6)

Plugging in the values, we get:

A = $18,000(1 + 0.01125/2)^(2 x 6)
A = $18,607.04

Finally, we subtract the principal from the total amount paid to get the interest cost:

Interest = $18,607.04 - $18,000
Interest = $607.04

Therefore, the answer is D) $607.04.

Sam Got a Job at the Brick