The difference between the simple interest and the compound interest on Rs. 600 for 1 year at 10% per annum, reckoned half yearly is :

Answer

To solve the problem of finding the difference between the simple interest (SI) and compound interest (CI) on Rs. 600 for 1 year at 10% 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:
- \( P = 600 \) (Principal)
- \( R = 10\% \) (Rate of interest)
- \( T = 1 \) year (Time)

Substituting the values:
\[ SI = \frac{600 \times 10 \times 1}{100} = \frac{6000}{100} = 60 \]
So, the Simple Interest (SI) is Rs. 60.

### 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-yearly compounding is \( \frac{10\%}{2} = 5\% \).
- The time for 1 year is \( 2 \) half-years.

The formula for Compound Interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Where:
- \( A \) = Amount after time \( n \)
- \( P = 600 \) (Principal)
- \( R = 10\% \) (Annual rate)
- \( n = 2 \) (Number of half-years)

Substituting the values:
\[ A = 600 \left(1 + \frac{5}{100}\right)^2 = 600 \left(1 + 0.05\right)^2 = 600 \left(1.05\right)^2 \]
Calculating \( (1.05)^2 \):
\[ (1.05)^2 = 1.1025 \]
Now, substituting back to find \( A \):
\[ A = 600 \times 1.1025 = 661.5 \]
Now, the Compound Interest (CI) can be calculated as:
\[ CI = A - P = 661.5 - 600 = 61.5 \]

### Step 3: Find the Difference between CI and SI
Now, we find the difference between Compound Interest and Simple Interest:
\[ \text{Difference} = CI - SI = 61.5 - 60 = 1.5 \]

### Final Answer
The difference between the simple interest and the compound interest is Rs. 1.5.

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