Compound Interest Rate Calculation

This question asks for the rate of interest when a sum of money triples in 3 years under compound interest.

Compound Interest Formula

The formula for compound interest is:

$ A = P \left(1 + \frac{R}{100}\right)^n $

• \(A\) = Amount after \(n\) years
• \(P\) = Principal amount
• \(R\) = Annual interest rate (in %)
• \(n\) = Number of years

Applying the Given Information

We are given:

• The amount becomes three times the principal: \(A = 3P\)
• The time period: \(n = 3\) years

Substituting these into the formula:

$ 3P = P \left(1 + \frac{R}{100}\right)^3 $

Solving for the Interest Rate (R)

1. Divide both sides by \(P\):

   $ 3 = \left(1 + \frac{R}{100}\right)^3 $

2. Take the cube root of both sides:

   $ \sqrt[3]{3} = 1 + \frac{R}{100} $

3. Calculate the cube root of 3:

   $ \sqrt[3]{3} \approx 1.44225 $

4. Substitute the value back:

   $ 1.44225 = 1 + \frac{R}{100} $

5. Solve for \(\frac{R}{100}\):

   $ \frac{R}{100} = 1.44225 - 1 $

   $ \frac{R}{100} = 0.44225 $

6. Solve for \(R\):

   $ R = 0.44225 \times 100 $

   $ R = 44.225\% $

Conclusion

The calculated interest rate is approximately 44.225%. Comparing this with the options, Option 1 (44.20%) is the closest match.