What will be the difference between simple interest and compound interest at 4% per annum on as sum of ₹5000 after 3 yr?

Options

A. ₹24.32
B. ₹28.56
C. ₹32.48
D. ₹36.18

Explanation

To find the difference between simple interest (SI) and compound interest (CI) on a sum of ₹5000 at a rate of 4% per annum after 3 years, we can follow these steps:

### Step 1: Calculate Simple Interest (SI)
The formula for calculating simple interest is:

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \( P \) = Principal amount (₹5000)
- \( R \) = Rate of interest (4%)
- \( T \) = Time period (3 years)

Substituting the values:

\[ SI = \frac{5000 \times 4 \times 3}{100} \]

Calculating this:

\[ SI = \frac{60000}{100} = 600 \]

So, the simple interest is ₹600.

### Step 2: Calculate Compound Interest (CI)
The formula for calculating compound interest is:

\[ CI = A - P \]

Where \( A \) (the amount) is calculated using the formula:

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

Substituting the values:

\[ A = 5000 \left(1 + \frac{4}{100}\right)^3 \]

Calculating \( 1 + \frac{4}{100} = 1 + 0.04 = 1.04 \):

Now, we calculate \( A \):

\[ A = 5000 \times (1.04)^3 \]

Calculating \( (1.04)^3 \):

\[ (1.04)^3 = 1.124864 \]

Now substituting back to find \( A \):

\[ A = 5000 \times 1.124864 = 5624.32 \]

Now, we can find the compound interest:

\[ CI = A - P = 5624.32 - 5000 = 624.32 \]

So, the compound interest is ₹624.32.

### Step 3: Calculate the Difference Between CI and SI
Now we find the difference between compound interest and simple interest:

\[ \text{Difference} = CI - SI = 624.32 - 600 \]

Calculating this:

\[ \text{Difference} = 24.32 \]

### Final Answer
The difference between simple interest and compound interest after 3 years is ₹24.32.

---