Math Growth and decay Percentage growth

# Percentage growth

Exponential growth also exists when there is an increase with a constant percentage growth rate.
The corresponding equation looks like this:

$N(t)=N_{0}\cdot (1+\frac{p}{100})^t$

At percentage decrease, however, the equation is as follows:

$N(t)=N_{0}\cdot (1-\frac{p}{100})^t$

$t...$ Period of time
$p ...$ Growth rate in %
$(1+\frac{p}{100}) ...$ Growth factor
$N(t) ...$ Value in dependence on $t$
$N_{0} ...$ Initial amount

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### Application

Particularly important is percentage growth in interest calculation. Then $N_{0}$ is the starting capital, $p$ the interest per year and $t$ the year.

### Example

With a bank you get 2% interest annually, if you invest 20 000 € for 5 years. Calculate the money after 5 years.

1. #### Determine values from the task

$t=5$
$p=2$
$N_{0}=20000$
2. #### Insert values in the formula

$N(\color{purple}{t})=\color{red}{N_{0}}\cdot (1+\frac{\color{green}{p}}{100})^\color{purple}{t}$
$N(\color{purple}{5})=\color{red}{20\,000}\cdot (1+\frac{\color{green}{2}}{100})^\color{purple}{5}$
3. #### Calculate and give result:

$N(5)\approx22\,082$

After 5 years you will have about 22 082 €.

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### Info

You can also find more about the percentage and interest calculation, especially the interest calculation, in the associated article.