# Find the total percentage loss over a specified time frame.

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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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