A piece of machinery valued at $250,000 depreciates at a fixed rate of 12% per year. After how many years will the value have depreciated to $100,000?

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Answer 1 · 2016-02-04T13:47:02

#7.17" years "#to 2 decimal places

Let the principle sum be #P=$250,000#

Let the final value after depreciation be #v=$100,000#
Let the number of years be #n#

Then

#v=p(1-12/100)^n" "->" "100000=250000(1-12/100)^n#

#=> (88/100)^n=100000/250000#

Taking logs

#nlog(0.88)=log(0.4)#

#n=(log(0.4))/(log(0.88))= 7.17" years "#to 2 decimal places