Question

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?

Answer 1

`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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`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)`