Calcualte the C.I. on Rs 3,500 at 6% per annum for 3 years, the interest being compounded half-yearly.
Do not use mathematical tables. Use the necessary information from the following:
`(1*06)^(3)=1*19106,(1*03)^(3)=1*092727`
`(1*06)^(6)=1*418519,(1*03)^(6)=1*194052`

Answer

To calculate the compound interest (C.I.) on Rs 3,500 at a rate of 6% per annum for 3 years, with interest being compounded half-yearly, we will follow these steps:

### Step 1: Identify the Principal, Rate, and Time
- Principal (P) = Rs 3,500
- Annual Rate of Interest (R) = 6%
- Time (T) = 3 years

### Step 2: Adjust the Rate and Time for Half-Yearly Compounding
Since the interest is compounded half-yearly:
- Rate per half-year = \( \frac{6\%}{2} = 3\% \)
- Total number of half-year periods in 3 years = \( 3 \times 2 = 6 \)

### Step 3: Use the Compound Interest Formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
Where:
- \( A \) = Amount after time \( t \)
- \( P \) = Principal
- \( r \) = Rate of interest per period
- \( t \) = Total number of periods

Substituting the values:
\[ A = 3500 \left(1 + \frac{3}{100}\right)^6 \]
\[ A = 3500 \left(1.03\right)^6 \]

### Step 4: Calculate \( (1.03)^6 \)
From the provided information, we know:
\[ (1.03)^6 = 1.194052 \]

### Step 5: Calculate the Amount
Now substituting this back into the amount formula:
\[ A = 3500 \times 1.194052 \]
Calculating this gives:
\[ A = 4179.18 \]

### Step 6: Calculate the Compound Interest
The compound interest (C.I.) is given by:
\[ C.I. = A - P \]
Substituting the values:
\[ C.I. = 4179.18 - 3500 \]
\[ C.I. = 679.18 \]

### Final Answer
The compound interest on Rs 3,500 at 6% per annum for 3 years, compounded half-yearly, is Rs 679.18.

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