# Sara agrees to buy a car for a down payment of $3000 and payments of$315 per month for 4 years. If the interest rate is 4.25% per year, compounded monthly, what is the actual purchase price of the car?

Nov 25, 2016

color(brown)("Full pre interest price "=$15760.00) #### Explanation: $\textcolor{b l u e}{\text{Down payment}}$color(blue)($3000)

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$\textcolor{b l u e}{\text{Determine the selling price above the down payment}}$

Let the actual selling price after down payment be $P$

Annual interest is $\frac{4.25}{100}$

Split over 12 months this is $\frac{4.25}{1200}$ per monthly payment

4 years is $4 \times 12 = 48$ months

So we have:

P(1+4.25/1200)^(48)=$315xx12xx4 $\log \left(P\right) + 48 \log \left(1 + \frac{4.25}{1200}\right) = \log \left(15120\right)$color(blue)(=>P =$12760.04)

There is scope for a slight difference due to inherent errors in calculator algorithms.
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$\textcolor{b l u e}{\text{Determine total price pre interest}}$

$12760.04" "+" "$3000" "=" "$15760.04 Due to anticipated errors in the calculator round this to: color(brown)($15760.00)