A startup company invested ₹ 5,00,000 in shares for 4 years. The value of the investment was ₹ 5,50,000 at the end of first year, ₹ 5,25,000 at the end of third year, and on maturity, the final value stood ₹ 6,25,000. The CAGR on the investment will be :- [Given : $(1.25)^{\frac{1}{4}} = 1.06$]

CAGR stands for Compound Annual Growth Rate. It tells us the average rate at which an investment grows each year over a period of time.

Don't worry about the ups and downs in between years - CAGR only cares about the starting value, final value, and time period.

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Let's pick out the important information:

Initial Investment $= ₹ 5,00,000$

Final Value $= ₹ 6,25,000$

Time Period $= 4$ years

The values at the end of 1st year $(₹ 5,50,000)$ and 3rd year $(₹ 5,25,000)$ are given to confuse you! Ignore them - they're not needed for CAGR calculation.

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The formula for CAGR is:

$\text{CAGR} = \left(\frac{\text{Final Value}}{\text{Initial Value}}\right)^{\frac{1}{\text{Time Period}}} - 1$

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Plugging in the values:

$\text{CAGR} = \left(\frac{6,25,000}{5,00,000}\right)^{\frac{1}{4}} - 1$

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Simplifying the fraction by canceling zeros:

$\frac{6,25,000}{5,00,000} = \frac{625}{500} = \frac{125}{100} = 1.25$

So now we have:

$\text{CAGR} = (1.25)^{\frac{1}{4}} - 1$

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The question tells us that $(1.25)^{\frac{1}{4}} = 1.06$

This saves us from complicated calculations! Just substitute:

$\text{CAGR} = 1.06 - 1 = 0.06$

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To convert to percentage, multiply by 100:

$\text{CAGR} = 0.06 \times 100 = 6\%$

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The CAGR on the investment is $6\%$

This means the investment grew at an average rate of $6\%$ per year over the 4-year period.