Same percentage increase, then decrease always ends in a lower number... Weird?

Question

Say you invest $100 in the stock market. It goes up by 10% (now $110). The stock then reduces by 10% from the new value (now $99). If you do the same in the opposite order (reduce 10%, then add 10%), you get the same result of $99. So, why doesn't it get back to $100 or perhaps $101? Why is it always less then you started?

Answer 1

Think about this:  20% of 300 is less than 20% of 350.  Thus, if you increase 300 by 20%

then decrease the new number by 20%, the decrease is a larger number, so the final 

difference is less than the original number.  Not so hard to understand.  :-)

 

The same thing works in reverse.  You take away more, then add less when you decrease

by 10% to a smaller number then add back 10% of the new number, you are adding less 

than you took away.

 

300 increased by 20% = 1.2(300) = 360

360 - 20% = 80% of 360 = 0.8(360) = 288

 

360 - 20% = 0.8(300) = 240

240 + 20% = 1.2(240) = 288