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Repeated percentage change

A change in percentage can be repeated several times.

The money I invest in a savings account increases by $$4\%$$ each year due to interest payment.

For a yearly percentage change of $$\Tred{p\%}$$, the new value $$\Tgreen{N}$$ after $$\Torange{n}$$ years from an old value $$\Tblue{O}$$ is $$ \Tgreen{N} = \Tblue{O} \times (1+\Tred{\frac{p}{100}})^\Torange{n}. $$

I invest $$\Tblue{1000}$$ in a bank account with an interest rate of $$\Tred{4\%}$$. After $$\Torange{3}$$ years, I will have a balance of $$\Tblue{1000} \times (1 + \Tred{4\%})^\Torange{3} = \Tblue{1000} \times 1\Tred{.04}^\Torange{3} = \Tblue{1000}\times 1.125 = \Tgreen{1125}.$$

 The population in this bacterial colony doubles every generation, an increase of 100%.
The population in this bacterial colony doubles every generation, an increase of 100%.