Theory:

In our day to day life, we observe that there are some situations or things that increase in magnitude over a period of time.
 
For example:
  
  • The population of a state/country.
  • The value of the property.
  • The growth of the cell.
  • The depreciation in the values of machines, vehicles, etc.,
 
Similar to the compound interest, the things  mentioned above will also increase over a period.
 
Let us learn how the compound interest formula is used to calculate these things.
1. Increase in Growth:
Type 1: Population growth after \(n\) years:
Let \(P\) be the population of a city or state at the beginning of a certain year, and the population grows at a constant rate of \(r \%\) per annum.
 
Then, the population after \(n\) years is given by A=P1+r100n.
Type 2: Population grows at different rates:
Let \(P\) be the population of a city or state at the beginning of a certain year, and the population grows at a constant rate of \(r_{1} \%\) in the first year, \(r_{2} \%\) in the second year and so on. 
 
Then, the population after \(n\) years is given by:
 
A=P1+r11001+r21001+r3100......1+rn100
2. Depreciation:
Let \(P\) be the value of the product or an article at a certain time, and the value of the product depreciates at the rate of \(r \%\) per annum.
 
Then, the depreciated value at \(n\) years is given by A=P1r100n.
Important!
We can also use the above formulae to calculate the growth of cells in a particular period at a particular rate and to calculatethe value of land increased or decreased at a particular time at a particular rate.