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?

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Answer 1 · 2017-07-23T09:08:32

$$44236.80$

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

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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$color(white)()$

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

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)=$44337.13$