Simple Interest to Compound Interest Calculation

The question asks for the compound interest (CI) on a sum, given the simple interest (SI) details for the same sum, rate, and time period.

Calculate Principal from Simple Interest

First, we need to find the principal amount (P) using the given simple interest (SI), rate (R), and time (T).

• SI = ₹50
• Rate (R) = 5% per annum
• Time (T) = 2 years

The formula for Simple Interest is:

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

Substitute the given values:

$ 50 = \frac{P \times 5 \times 2}{100} $

$ 50 = \frac{P \times 10}{100} $

$ 50 = \frac{P}{10} $

Solve for P:

$ P = 50 \times 10 $

$ P = 500 $

The principal sum is ₹500.

Calculate Compound Interest

Now, we calculate the compound interest (CI) for the same principal, rate, and time.

• Principal (P) = ₹500
• Rate (R) = 5% per annum
• Time (T) = 2 years

The formula for Compound Interest is:

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

Substitute the values:

$ CI = 500 \left(1 + \frac{5}{100}\right)^2 - 500 $

$ CI = 500 \left(1 + 0.05\right)^2 - 500 $

$ CI = 500 \left(1.05\right)^2 - 500 $

Calculate the square of 1.05:

$ (1.05)^2 = 1.1025 $

Continue the calculation for CI:

$ CI = 500 \times 1.1025 - 500 $

$ CI = 551.25 - 500 $

$ CI = 51.25 $

The compound interest is ₹51.25.