Question

9. A car dealership offers a loan with 4% interest for 48 months, and you plan to purchase a car for $20,000. You can afford a down payment of $2,500.(a) What will your monthly payment be? $(b) How much will you pay in total for the car? $(c) How much will you pay in interest over the life of the loan? $

Answer 1

SOLUTION

Since you can afford a down payment of $2,500, the remaining money needed to purchase the car becomes

$\begin{gathered} 20,000-2,500 \\ =17,500 \end{gathered}$

Now, we will find the simple interest on $17,500 for 48 months, which is 4 years. This becomes

$\begin{gathered} I=\frac{PRT}{100} \\ I=\frac{17,500\times4\times4}{100} \\ I=2,800\text{ dollars } \end{gathered}$

(a) What will your monthly payment be? $

We will add this interest to the $17,500 and divide by 48 months to get the monthly payment. This becomes

$\begin{gathered} 17,500+2,800=20,300 \\ \frac{20,300}{48}=422.91666 \\ =422.92 \end{gathered}$

Hence, the answer is $422.92

(b) How much will you pay in total for the car? $

To get this, we add the $20,300 (that we divided by 48 months), to the initial down payment made. This becomes

$\begin{gathered} 20,300+2500 \\ =22,800 \end{gathered}$

Hence, the answer is $22,800

(c) How much will you pay in interest over the life of the loan? $

We have initially found the interest as 2,800 dollars.

Hence the answer is $2,800