The difference between simple and compound interest on Rs 1,000 for 3 years at 5% p.a. interest is:

Options

A. Rs `8.40`
B. Rs `10.15`
C. Rs `7.60`
D. Rs `9.20`

Answer

To find the difference between simple interest (SI) and compound interest (CI) on Rs 1,000 for 3 years at a rate of 5% per annum, we will follow these steps:

### Step 1: Calculate Compound Interest (CI)
The formula for the amount (A) in compound interest is:

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

Where:
- \(P\) = Principal amount = Rs 1,000
- \(R\) = Rate of interest = 5%
- \(T\) = Time in years = 3

Substituting the values:

\[ A = 1000 \left(1 + \frac{5}{100}\right)^3 \]

This simplifies to:

\[ A = 1000 \left(1.05\right)^3 \]

Calculating \(1.05^3\):

\[ 1.05^3 = 1.157625 \]

Now, calculate the total amount:

\[ A = 1000 \times 1.157625 = 1157.625 \]

### Step 2: Calculate Compound Interest (CI)
Now, we find the compound interest (CI) by subtracting the principal from the total amount:

\[ CI = A - P = 1157.625 - 1000 = 157.625 \]

### Step 3: Calculate Simple Interest (SI)
The formula for simple interest is:

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

Substituting the values:

\[ SI = \frac{1000 \times 5 \times 3}{100} \]

This simplifies to:

\[ SI = \frac{15000}{100} = 150 \]

### Step 4: Calculate the Difference between CI and SI
Now, we find the difference between compound interest and simple interest:

\[ \text{Difference} = CI - SI = 157.625 - 150 = 7.625 \]

### Conclusion
The difference between simple interest and compound interest on Rs 1,000 for 3 years at 5% per annum is approximately Rs 7.63.

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