Govind's Investment: Simple Interest Calculation

This solution explains how to calculate the simple interest Govind would receive on his investment, given the compound interest earned over 2 years at a specific rate.

Understanding the Goal

The main objective is to find the simple interest (SI) for Govind's investment. We are given the compound interest (CI), the annual interest rate (R), and the time period (T).

Key Information Provided

• Rate of Interest (R): 4% per annum
• Time Period (T): 2 years
• Compound Interest Earned (CI): ₹280.5

Calculating the Principal Amount (P)

To find the simple interest, we first need to determine the initial amount Govind invested, which is the principal (P). We can use the compound interest formula for this. The formula for compound interest is:

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

Let's plug in the known values:

• $CI = 280.5$
• $R = 4$
• $T = 2$

Substituting these into the formula:

$$ 280.5 = P \left[ \left(1 + \frac{4}{100}\right)^2 - 1 \right] $$

Simplify the expression inside the brackets:

$$ 280.5 = P \left[ \left(1 + 0.04\right)^2 - 1 \right] $$

$$ 280.5 = P \left[ (1.04)^2 - 1 \right] $$

Calculate $(1.04)^2$:

$$ (1.04)^2 = 1.0816 $$

Now substitute this back:

$$ 280.5 = P [ 1.0816 - 1 ] $$

$$ 280.5 = P [ 0.0816 ] $$

To find the Principal (P), rearrange the equation:

$$ P = \frac{280.5}{0.0816} $$

Calculating the value of P:

$$ P = 3437.5 $$

So, the principal amount Govind invested was ₹3437.5.

Calculating the Simple Interest (SI)

Now that we have the principal amount, we can calculate the simple interest using the formula:

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

Using the values we have:

• $P = 3437.5$
• $R = 4$
• $T = 2$

Substitute these values into the SI formula:

$$ SI = \frac{3437.5 \times 4 \times 2}{100} $$

$$ SI = \frac{3437.5 \times 8}{100} $$

$$ SI = \frac{27500}{100} $$

$$ SI = 275 $$

Final Answer Explanation

The calculated simple interest for Govind's investment over 2 years at a 4% annual rate is ₹275.