Find the difference between the simple and compound interest on Rs. 8000 for 3 years at 5 percent.

Answer

To find the difference between the simple interest (SI) and compound interest (CI) on Rs. 8000 for 3 years at a rate of 5%, we can use the formula for the difference between CI and SI for 3 years, which is given by:

\[ \text{Difference} = P \times \frac{R}{100} \times \left( \frac{R}{100} + 3 \right) \]

Where:
- \( P \) = Principal amount (Rs. 8000)
- \( R \) = Rate of interest (5%)

### Step 1: Substitute the values into the formula

Substituting the values into the formula, we have:

\[ \text{Difference} = 8000 \times \frac{5}{100} \times \left( \frac{5}{100} + 3 \right) \]

### Step 2: Simplify the expression

First, calculate \( \frac{5}{100} \):

\[ \frac{5}{100} = 0.05 \]

Now, substitute this back into the equation:

\[ \text{Difference} = 8000 \times 0.05 \times (0.05 + 3) \]

Calculating \( 0.05 + 3 \):

\[ 0.05 + 3 = 3.05 \]

Now, substitute this back into the equation:

\[ \text{Difference} = 8000 \times 0.05 \times 3.05 \]

### Step 3: Calculate the multiplication

Now, calculate \( 8000 \times 0.05 \):

\[ 8000 \times 0.05 = 400 \]

Now, multiply this result by 3.05:

\[ \text{Difference} = 400 \times 3.05 \]

Calculating \( 400 \times 3.05 \):

\[ 400 \times 3.05 = 1220 \]

### Step 4: Final calculation

Now, we have:

\[ \text{Difference} = 1220 \]

### Conclusion

The difference between the simple interest and compound interest on Rs. 8000 for 3 years at 5% is Rs. 1220.

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