Application of compound interest — lesson. Mathematics State Board, Class 8.

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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 = P {(1 + \frac{r}{100})}^{n}

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 = P (1 + \frac{r_{1}}{100}) (1 + \frac{r_{2}}{100}) (1 + \frac{r_{3}}{100}) ... ... (1 + \frac{r_{n}}{100})

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 = P {(1 - \frac{r}{100})}^{n}

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.

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4. Application of compound interest

Theory: