The difference between simple and compound interest on Rs. 6000 for 1 year at 20% per annum reckoned half yearly is :

Options

A. 120
B. 60
C. 180
D. 72

Answer

To find the difference between simple interest (SI) and compound interest (CI) on Rs. 6000 for 1 year at 20% per annum, compounded half-yearly, we will follow these steps:

### Step 1: Calculate Simple Interest (SI)
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P = 6000 \) (Principal)
- \( R = 20\% \) (Rate of interest)
- \( T = 1 \) year

Substituting the values:
\[ SI = \frac{6000 \times 20 \times 1}{100} = \frac{120000}{100} = 1200 \]

### Step 2: Calculate Compound Interest (CI)
Since the interest is compounded half-yearly, we need to adjust the rate and time:
- The rate for half a year is \( \frac{20}{2} = 10\% \)
- The time for 1 year is \( 2 \) half-year periods.

The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Where:
- \( n = 2 \) (number of compounding periods)

Calculating \( A \):
\[ A = 6000 \left(1 + \frac{10}{100}\right)^2 = 6000 \left(1 + 0.1\right)^2 = 6000 \left(1.1\right)^2 \]
Calculating \( (1.1)^2 \):
\[ (1.1)^2 = 1.21 \]
Now substituting back:
\[ A = 6000 \times 1.21 = 7260 \]

Now, we can find the compound interest (CI):
\[ CI = A - P = 7260 - 6000 = 1260 \]

### Step 3: Calculate the Difference between CI and SI
Now, we can find the difference:
\[ \text{Difference} = CI - SI = 1260 - 1200 = 60 \]

### Final Answer
The difference between simple and compound interest on Rs. 6000 for 1 year at 20% per annum reckoned half-yearly is **Rs. 60**.

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