So I had ₹100 and in six years became ₹300 assuming there was a equal growth every year equal percentage growth so what's the annual CAGR

Answer: The annual CAGR is approximately 20.09%.

Step-by-step solution

Step 1: Understand Compound Annual Growth Rate (CAGR)

The Compound Annual Growth Rate (CAGR) is the annual rate of return that makes an initial investment grow to a final value over a specified period. The formula for compound interest is $A = P(1 + r)^n$ , where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual growth rate (CAGR), and $n$ is the number of years.

Step 2: Identify Given Values

From the problem statement, we are given the initial amount (principal) as ₹100, the final amount as ₹300, and the number of years as 6. We need to find the annual growth rate, $r$ .

Step 3: Substitute Values into the Formula

Now, substitute the identified values into the compound interest formula. This gives us an equation where $r$ is the only unknown.

Step 4: Isolate (1 + r)

To solve for $r$ , first divide both sides of the equation by the principal amount, 100. This simplifies the equation to $3 = (1 + r)^6$ .

Step 5: Solve for r

To isolate $(1+r)$ , take the sixth root of both sides. Then, subtract 1 from the result to find $r$ . Calculating $(3)^{1/6}$ gives approximately 1.2009. Subtracting 1 yields $r \approx 0.2009$ .

Step 6: Convert to Percentage

Finally, convert the decimal value of $r$ to a percentage by multiplying by 100. This gives the Compound Annual Growth Rate (CAGR).