# How to Calculate Growth Factor

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Growth factor is a simplified way of calculating percentages. Previously, you have calculated percentages in several stages, finding the percentage first and then adding it to or subtracting it from the original number. With growth factor, you will learn to do this in one operation. Growth factor makes percentage calculation and percentage changes a lot easier, and saves you a lot of time.

Formula

, where $p$ is the percentage.

When increasing, use $\phantom{\rule{-0.17em}{0ex}}\left(1+\frac{p}{100}\right)$.

When reduction, use $\phantom{\rule{-0.17em}{0ex}}\left(1-\frac{p}{100}\right)$.

Let me explain the formula: Inside the parentheses you have a number one, plus or minus, and the fraction $\frac{p}{100}$. The number one represents what you should calculate the percentage of. Plus or minus tells you that you have two formulas in one: One formula for increases (plus), and one formula for decreases (minus) in value. $\frac{p}{100}$ is the usual percentage rule you are used to. Look closely at the connections in the box below.

Rule

### Interpretationofthegrowthfactor

• You have an increase if the growth factor is greater than one, $>1$.

• You have a reduction if the growth factor is less than one, $<1$.

Example 1

If something increases by $25$ %, the growth factor will be

 $\phantom{\rule{-0.17em}{0ex}}\left(1+\frac{25}{100}\right)=1+0.25=1.25$

If something decreases by $20$ %, the growth factor will be

 $\phantom{\rule{-0.17em}{0ex}}\left(1-\frac{20}{100}\right)=1-0.2=0.8$

Example 2

The growth factor if an investment increases by $10$ %:

 $\phantom{\rule{-0.17em}{0ex}}\left(1+\frac{10}{100}\right)=1+0.1=1.1$

The growth factor if an investment decreases by $10$ %:

 $\phantom{\rule{-0.17em}{0ex}}\left(1-\frac{10}{100}\right)=1-0.1=0.9$

An investment is an expense you have now, with an expectation that it will pay off in the future.