Question

Ben buys a car for $50,000. The value of the car decreases at a rate of 4% per year. How much will the car be worth in 3 years?

Answer 1

`$44236.80`

Explanation:

`color(blue)("Answering the question")`

This is the same sort of thing as compound interest.

Growth`->P(1+x%)^n`
Decay`->P(1-x%)^n`

This question requires decay.

Assumption: The calculation cycle is annually.

`$50000(1-4/100)^3`

`$50000(96/100)^3 = $44236.80`

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`color(blue)("Just for interest sake")`

Note that if the calculation cycle was monthly then the change is:

As there are 12 months in 1 year we use the percentage `(x%)/12`

And the `n` value becomes `12n`

`$50000(1-4/(12xx100))^(12xx3)`

`$50000(1-(cancel(4)^1)/(cancel(12)^3xx100))^(12xx3)`

`$50000(299/300)^(36)=$44337.13`