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

Options

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

Answer

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 Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount = 5000
- \( R \) = Rate of interest = 4%
- \( T \) = Time in years = 3

Substituting the values:
\[ SI = \frac{5000 \times 4 \times 3}{100} = \frac{60000}{100} = 600 \]

### Step 2: Calculate Compound Interest (CI)
The formula for Compound Interest is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
Substituting the values:
\[ CI = 5000 \left(1 + \frac{4}{100}\right)^3 - 5000 \]
\[ = 5000 \left(1 + 0.04\right)^3 - 5000 \]
\[ = 5000 \left(1.04\right)^3 - 5000 \]

Calculating \( (1.04)^3 \):
\[ (1.04)^3 = 1.124864 \]
Now substituting this back:
\[ CI = 5000 \times 1.124864 - 5000 \]
\[ = 5624.32 - 5000 = 624.32 \]

### Step 3: Calculate the Difference between CI and SI
Now, we find the difference between Compound Interest and Simple Interest:
\[ \text{Difference} = CI - SI = 624.32 - 600 = 24.32 \]

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

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