Compound growth and decay

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Summary

Compound growth and decay

​​In a nutshell

Compound growth and decay (commonly used to work out compound interest) involves percentage changes over a period of time - usually on a yearly basis. 



Compound growth and decay formula

In order to calculate compound growth and decay, a formula must be used:


Amount after n time=initial amount×(percentage change multiplier)n\text{Amount after n time} = \text{initial amount} \times \text{(percentage change multiplier)}^n


This is sometimes written as:

N=N0×(multiplier)nN = N_0 \times (\text{multiplier})^n​​



Note: n could be time in years, months, days or any time period you can think of!


Example 1

Mitchell bought a car for £10,500£10,500. It depreciates in value by 12%12\% each year. How much will the car be worth in six years time?


Work out the multiplier.

10.12=0.881-0.12=0.88


Use the formula.

Amount after six years =10500×(0.88)6=£4876.24= 10500\times(0.88)^6 = \underline{£4876.24} (rounded to two decimal places.)​


Example 2

The panda population is decreasing by two percent every year. The current population is 50005000. What was the population three years ago? (Round your answer to the nearest whole number).


Work out the multiplier.

10.02=0.981-0.02=0.98​​


Fill in the formula with what you know where xx is the population three years ago.

7500=x×(0.98)37500=x\times(0.98)^3​​


Rearrange and solve for xx.

7500=x×(0.98)3÷(0.98)3÷(0.98)37968.62=x\begin {aligned}&&7500&=x\times(0.98)^3 \\\div(0.98)^3&&&&\div (0.98)^3 \\&&7968.62&=x\end {aligned}


Round to the nearest whole number.

7968.6279697968.62 \dashrightarrow \underline{7969}


The population three years ago was 7969\underline{7969} pandas.




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