## Increase numbers by percentage of their initial value and calculate the absolute percentage change (difference)

### How to calculate the new value of a number when increasing it by percentage of its initial value and how to calculate the absolute percentage change (difference)?

- New value = Initial value + Absolute percentage change (difference)
- Absolute percentage change (difference) = Percentage increase % × Initial value
- => New value = Initial value + Percentage increase % × Initial value = (1 + Percentage increase %) × Initial value
- In conclusion:
#### New value = (1 + Percentage increase %) × Initial value

#### Initial value = New value / (1 + Percentage increase %)

#### Absolute percentage change (difference) = Percentage increase % × Initial value = New value - Initial value

### Examples of calculations on how to increase a number by percentage of its initial value (percentage increase) and calculate the absolute percentage change (difference):

- If Percentage increase % = 20%, (1 + Percentage increase %) = 1 + 20% = 100/100 + 20/100 = 120/100 = 1.20 =>
**Number increased by value percentage**= 1.20 × Initial value, and**Initial value**= Number increased by value percentage / 1.20;**Absolute percentage change**= New value - Initial value; - If Percentage increase % = 5%, (1 + Percentage increase %) = 1 + 5% = 100/100 + 5/100 = 105/100 = 1.05 =>
**Number increased by value percentage**= 1.05 × Initial value, and**Initial value**= Number increased by value percentage / 1.05;**Absolute percentage change**= New value - Initial value; - If Percentage increase % = 124%, (1 + Percentage increase %) = 1 + 124% = 100/100 + 124/100 = 224/100 = 2.24 =>
**Number increased by value percentage**= 2.24 × Initial value, and**Initial value**= Number increased by value percentage / 2.24;**Absolute percentage change**= New value - Initial value; - If Percentage increase % = -8%, (1 + Percentage increase %) = 1 - 8% = 100/100 - 8/100 = 92/100 = 0.92 =>
**Number increased by value percentage**= 0.92 × Initial value, and**Initial value**= Number increased by value percentage / 0.92; in this case we have in fact a decreasing of the value of the number;**Absolute percentage change**= New value - Initial value.