The Question
Anna buys a car by paying 10% down and by financing the balance with a loan at 15%/a, compounded monthly, to amortize the loan by making monthly payments of $225 each month for 3 years. Determine the sale price.
a. $6490.64
b. $7932.36
c. $7211.82
d. $8821.18
Using Present Value formula:
$$PV=R\cdot \frac{1-\left ( 1+i \right )^{-n}}{i}\\
PV=225\cdot \frac{1-\left ( 1+0.0125 \right )^{-36}}{0.0125}\\
PV=225\cdot \frac{1-\left ( 0.639409157 \right )}{0.0125}\\
PV=225\cdot \frac{0.360590842}{0.0125}\\
PV=225\cdot 28.84726737\\
PV=\$ 6490.64$$
However, this does not account for the 10% downpayment.
Calculating 10% of each answer option, allows me to conclude $7211.82 is the answer:
$$$7211.82\cdot 0.10=$721.18\\
\$ 6490.64+$721.18=\$ 7211.82$$
I'm not sure how I would have been able to come to the same conclusion without seeing the answers.
How can I calculate the downpayment with the given information?
Let $x$ be the sale price. Simply set $6490.64 = x - 0.1x$, or $6490.64 = 0.9x.$ I'm sure you can take it from there.