Finding Principal Sum from Compound Interest

We are given the Compound Interest (CI), rate (R), and time period (n). We need to find the principal sum (P) first.

• CI = ₹864
• Rate (R) = 20% per annum
• Period (n) = 3 years

The formula for Compound Interest is:

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

Substitute the given values:

$ 864 = P \times \left( \left(1 + \frac{20}{100}\right)^3 - 1 \right) $

$ 864 = P \times \left( \left(1 + 0.2\right)^3 - 1 \right) $

$ 864 = P \times \left( (1.2)^3 - 1 \right) $

$ 864 = P \times (1.728 - 1) $

$ 864 = P \times 0.728 $

Now, solve for P:

$ P = \frac{864}{0.728} $

$ P \approx 1186.81 $

Calculating Simple Interest

Now we use the principal sum (P) found above to calculate the Simple Interest (SI) for the same rate and period.

• Principal (P) ≈ ₹1186.81
• Rate (R) = 20% per annum
• Period (n) = 3 years

The formula for Simple Interest is:

$ SI = \frac{P \times R \times n}{100} $

Substitute the values:

$ SI = \frac{1186.81 \times 20 \times 3}{100} $

$ SI = \frac{1186.81 \times 60}{100} $

$ SI = 1186.81 \times 0.6 $

$ SI \approx 712.086 $

Rounding to two decimal places, the Simple Interest is ₹712.09.