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
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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≈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).