The chart shows the losses and gains in an investment over the course of five years. What was the average growth rate over the course of the five years?

Year$\space\space\space$ Percent Growth






I thought that this would mean that if you start with a value of $x$, then the each percentage represents an increase in the previous amount. This would mean that the final amount after 5 years is $x\times1.10\times.97\times.92\times1.04\times1.06$ or $1.0822x$

This would mean that the percent increase is $8.22\%$, but the real answer is $1.59\%$. How would this "average" work and how is my work wrong in the first place?


You are correct that at the end of year five the amount is $1.0822$ times larger than the start value. If you want the average annual growth rate, you take the $1/5$ power of this, as this will be the annual growth that when repeated fve times gives a factor $1.0822$. In fact $1.0822^{1/5} \approx 1.01592$


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