Finding Principal from Compound Interest

The formula for compound interest (CI) is:

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

We are given:

• CI = ₹6,305
• Rate (R) = 5% per annum
• Time (T) = 3 years

Substitute the values into the formula to find the Principal (P):

$ 6305 = P \left[ \left(1 + \frac{5}{100}\right)^3 - 1 \right] $

$ 6305 = P \left[ \left(1 + 0.05\right)^3 - 1 \right] $

$ 6305 = P \left[ (1.05)^3 - 1 \right] $

Calculate $(1.05)^3$:

$ (1.05)^3 = 1.157625 $

Now, substitute this back:

$ 6305 = P \left[ 1.157625 - 1 \right] $

$ 6305 = P \left[ 0.157625 \right] $

Solve for P:

$ P = \frac{6305}{0.157625} $

$ P = 40000 $

So, the principal sum is ₹40,000.

Calculating Simple Interest

Now, we need to find the simple interest (SI) for the same principal, rate, and time.

The formula for simple interest is:

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

Using the calculated principal (P = ₹40,000), R = 5%, and T = 3 years:

$ SI = \frac{40000 \times 5 \times 3}{100} $

$ SI = 400 \times 5 \times 3 $

$ SI = 2000 \times 3 $

$ SI = 6000 $

The simple interest is ₹6,000.