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If you had an investment and you consistently lost 5% of it per year for 6 years, how do you find the total percentage loss, without knowing the original investment?

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up vote 3 down vote accepted

Say that the amount of the original investment is $x$. Losing $5$% of it is multiplying it by $0.95$, so after the six years you’re down to $0.95^6x$, and you’ve lost $x-0.95^6x=\left(1-0.95^6\right)x$. As a fraction of your original investment this is

$$\frac{\left(1-0.95^6\right)x}x\;.$$

Now just simplify and convert to a percentage.

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Thanks! That worked perfectly. – Tyler Zika Dec 10 '12 at 6:00
    
@Tyler: You’re welcome! – Brian M. Scott Dec 10 '12 at 6:00

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