Calculating Principal Investment Amount

This problem involves finding the initial investment amount (principal) based on the difference between simple interest (SI) and compound interest (CI) earned over a specific period at a given rate.

Understanding the Variables

• Let the principal amount invested be denoted by '$P$'.
• The rate of interest ($R$) is 4% per annum.
• The time period ($T$) for both investments is 2 years.
• The difference between Compound Interest (CI) and Simple Interest (SI) is ₹43.

Calculating Simple Interest (SI)

The formula for Simple Interest is:

$$ \text{SI} = \frac{P \times T \times R}{100} $$

Substituting the given values:

$$ \text{SI} = \frac{P \times 2 \times 4}{100} = \frac{8P}{100} $$

Calculating Compound Interest (CI)

The formula for Compound Interest compounded annually is:

$$ \text{CI} = P \left(1 + \frac{R}{100}\right)^T - P $$

Substituting the given values:

$$ \text{CI} = P \left(1 + \frac{4}{100}\right)^2 - P $$

$$ \text{CI} = P (1.04)^2 - P $$

$$ \text{CI} = P (1.0816) - P $$

$$ \text{CI} = 0.0816P $$

Finding the Difference Between CI and SI

The problem states that the difference between CI and SI is ₹43.

$$ \text{CI} - \text{SI} = 43 $$

Substituting the calculated values for CI and SI:

$$ 0.0816P - \frac{8P}{100} = 43 $$

$$ 0.0816P - 0.08P = 43 $$

$$ 0.0016P = 43 $$

Solving for the Principal Amount (P)

To find the principal amount '$P$', we rearrange the equation:

$$ P = \frac{43}{0.0016} $$

$$ P = \frac{43}{16/10000} $$

$$ P = \frac{43 \times 10000}{16} $$

$$ P = \frac{430000}{16} $$

$$ P = 26875 $$

Conclusion

Therefore, the sum invested by Amit was ₹26,875.