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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%.