The price of a stock appreciated by 25.50% of its value last month and then depreciated by 25.50% this month.

Question

The price of a stock appreciated by 25.50% of its value last month and then depreciated by 25.50% this month. By what percent did the stock appreciate or depreciate over the 2-month period? Express your answer as a positive or negative value based on the direction of the percentage change.

Answer 1

100 +.25.5% of 100 = 100+25.5 = 125.5

125.5 - 25.5% of 125.5 = 125.5 - 32.0025 = 93.4975

from 100 to 125.5 to 93.4975 is a 6.5025% depreciation over two months

= about - 6.50 % change in value

if the reverse had happened, a 25.5% decrease followed by the following month a 25.5% increase

then the total change in value would have been 100 to 74.5 to 93.4975,

= the same -6.5025% change

try it with any other starting value, it's the same percentage decrease in value = - 6.50025%

$200 value then depreciate 25.5% to get 200-51 = 149, then appreciate 25.5% to get 149+ 37.995= 186.995

from 200 to 186.995 is a decrease of 13.005

-13.005/200 = -6.5025% change in value