Percent Increase
Value after a percentage increase.
Formula
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Example
$50 up 20% = $60
How it works
A percentage increase means you add a fraction of the original value onto itself. The formula new = old(1 + p) works because the original amount counts as 100% of the starting value, and the increase adds another p as a decimal; together that is 1 + p times the original. For example, a 15% increase means you keep 100% of the old amount and add 15% more, which is the same as multiplying by 1.15.
When to use it
Use this when a quantity grows by a fixed percentage, such as prices, salaries, populations, or measurements after growth. It is useful any time you know the starting value and the percent increase, and you want the new value.
Worked example, step by step
Start with old = 80 Increase by 25%, so p = 0.25 Use the formula: new = old(1 + p) new = 80(1 + 0.25) new = 80(1.25) new = 100 Final answer: the new value is 100
Common mistakes to avoid
- Using 25 instead of 0.25 for the percent increase
- Adding the percent directly to the old value instead of multiplying by 1 + p
- Forgetting that the percent increase is based on the original value, not the new value
Did You Know?
A 50% rise followed by a 50% fall does not return you to the start — you end up 25% below it, a trap that fools many investors.
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