The price of a stock falls by 23% then later rises by 23%. After the two changes in value the price is unchanged

Answer 1

Not true. It appears "reasonable," but it's false.

Use a specific example. The price of stock is $100

it falls 23% to $77. .23(100) = $23 fall. 100-23 =77

then it rises by 23%. .23(77)= $17.71

77+17.71 = $94.71, not $100

or in general, if the original stock price was P

then after a 23% fall, its new price is P-.23P = .77P

then after a 23% rise, its final price is .77P+.23(.77P) = (.77+.1771)P = .9471P < P