[ Percentage and ratio problems ]

Car: Zassovsky A.

An analyst made a forecast of the dollar exchange rate change for each of the next three months: by what percentage (a number greater than $0 \%$ and less than $100 \%$) the rate would change in July, by what percentage in August, and by what percentage in September. It turned out that for each month, he correctly predicted the percentage by which the rate would change, but
he was wrong about the direction of the change (that is, if he predicted that the rate would increase by x\%, the rate fell by x\%, and vice versa). At the same time, after three months, the rate matched the forecast. In which direction did the rate ultimately change?
Let's use fractions instead of percentages: the exchange rate changes by $x(00)$. Then, by the condition, $a=(1+x)(1+y)(1+z)=(1-x)(1-y)(1-z)$, from which $a^{2}=\left(1-x^{2}\right)\left(1-y^{2}\right)\left(1-z^{2}\right)<1$, and, consequently, $a<1$.

## Answer

It has decreased.