percent change (percent difference)
Percent increase and percent decrease are measures of percent change, which is the extent to which a variable gains or loses intensity, magnitude, extent, or value. The figures are arrived at by comparing the initial (or before) and final (or after) quantities according to a specific formula. It is assumed that both the initial and the final quantities are positive (larger than 0).
Suppose a quantity has an initial value of x1, and then increases or decreases to a final value of x2. The percent change, D%, is calculated by finding the difference x2  x1 (subtracting the initial value from the final value), then dividing the result of this subtraction by x1 (the initial value), and finally multiplying by 100. Expressed as a formula:
D% = 100 (x2  x1) / x1
If x2 > x1 (the final value is larger than the initial value, representing an increase in the variable quantity), then D% is a positive number. If x2 < x1 (the final value is smaller than the initial value, representing a decrease), then D% is a negative number.
As an example, suppose you buy stock in two companies A and B, both at a price of USD $1.25 per share in January of a given year. Suppose that by July, stock A has risen in value to USD $3.35 per share. Then for stock A:
DA% = 100 ($3.35  $1.25) / $1.25 = +168%
Percent change is +168%, also expressed as a percent increase of 168%.
Imagine that stock B has fallen to USD $1.00 per share in the same time period. Then for stock B:
DB% = 100 ($1.00  $1.25) / $1.25 = 20%
Percent change is 20%, also expressed as a percent decrease of 20%.
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