SOLUTION: A machine depreciates in value each year by 8% of its value at the beginning of the year. After how many years will its value first be less than half its original value?
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Question 984029: A machine depreciates in value each year by 8% of its value at the beginning of the year. After how many years will its value first be less than half its original value? Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! This is basically an interest problem with the percentage negative.
P=Po{1-0.08}^n
But P/P0=0.5, since it will be half as much.
0.5=1.08^n
take ln of both sides
0.693=n ln (1.08); ln (1.08)=0.07696 (rounded).
Not rounding,
divide by that.
9.006 years (rounded)
This is the rule of 72 in reverse.
