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?

1 Answer
Jul 23, 2017

#$44236.80#

Explanation:

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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 #