Question

kyle wishes to purchase a used car that has a cash price of $12,000. the installment terms include a down payment of $3,000 and 48 monthly payments of $224.

what finance charge will kyle pay?

what is the APR to the nearest half percent?

Answer 1

Using simple interest and the information given, it is found that:

• The finance charge was of $1,752.

• The APR was of 0.0365 = 3.65%.

• The cash price of the car is of $12,000.
• For they payment, there is a down payment of $3,000, plus 48 payments of $224, hence, the total payment is:

$P = 3000 + 48(224) = 13752$

The finance charge is the total payment subtracted by the cash price, hence:

$E = 13752 - 12000 = 1752$

The amount of simple interest accrued after t years, with an APR of r and an initial value of I, is:

$E = Irt$

For this problem, we have that $E = 1752, I = 12000, t = \frac{48}{12} = 4$, hence:

$E = Irt$

$1752 = 12000(4)r$

$r = \frac{1752}{48000}$

$r = 0.0365$

The APR was of 0.0365 = 3.65%.

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