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?

1 Answer
Nov 25, 2016

Answer:

#color(brown)("Full pre interest price "=$15760.00)#

Explanation:

#color(blue)("Down payment")#

#color(blue)($3000)#

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#color(blue)("Determine the selling price above the down payment")#

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

Annual interest is #4.25/100#

Split over 12 months this is #4.25/1200# per monthly payment

4 years is #4xx12 = 48# months

So we have:

#P(1+4.25/1200)^(48)=$315xx12xx4#

#log(P)+48log(1+4.25/1200) = log(15120)#

#color(blue)(=>P = $12760.04)#

There is scope for a slight difference due to inherent errors in calculator algorithms.
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#color(blue)("Determine total price pre interest")#

#$12760.04" "+" "$3000" "=" "$15760.04#

Due to anticipated errors in the calculator round this to:

#color(brown)($15760.00)#