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?

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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?

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Answer 1 · 2016-11-25T22:03:12

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

Explanation:

$color(blue)("Down payment")$

$color(blue)($3000)$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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

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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("Determine total price pre interest")$

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

Due to anticipated errors in the calculator round this to:

$color(brown)($15760.00)$

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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

Explanation:

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