Divakaran deposited a sum of Rs 6250 in the Allahabad Bank for 1 year, compunded half-yearly at 8% per annum. Find the compound interest he gets.

Answer

To solve the problem step by step, we will calculate the compound interest earned by Divakaran on his deposit of Rs. 6250 compounded half-yearly at an interest rate of 8% per annum for 1 year.

### Step 1: Identify the given values
- Principal (P) = Rs. 6250
- Rate of interest (R) = 8% per annum
- Time (T) = 1 year

Since the interest is compounded half-yearly, we need to adjust the rate and time accordingly.

### Step 2: Adjust the rate and time for half-yearly compounding
- The half-yearly rate of interest = R/2 = 8%/2 = 4%
- The number of compounding periods in 1 year = 2 (since it is compounded half-yearly)

### Step 3: Use the compound interest formula
The formula for compound interest when compounded multiple times a year is:
\[ A = P \left(1 + \frac{r}{100}\right)^{nt} \]
Where:
- \( A \) = Amount after time \( t \)
- \( P \) = Principal amount
- \( r \) = Rate of interest per compounding period
- \( n \) = Number of times interest is compounded per year
- \( t \) = Time in years

In our case:
- \( P = 6250 \)
- \( r = 4 \) (half-yearly rate)
- \( n = 2 \) (compounding twice a year)
- \( t = 1 \)

### Step 4: Substitute the values into the formula
\[ A = 6250 \left(1 + \frac{4}{100}\right)^{2 \times 1} \]
\[ A = 6250 \left(1 + 0.04\right)^{2} \]
\[ A = 6250 \left(1.04\right)^{2} \]

### Step 5: Calculate \( (1.04)^{2} \)
\[ (1.04)^{2} = 1.0816 \]

### Step 6: Calculate the amount \( A \)
\[ A = 6250 \times 1.0816 \]
\[ A = 6760 \]

### Step 7: Calculate the compound interest (CI)
The compound interest is given by:
\[ CI = A - P \]
\[ CI = 6760 - 6250 \]
\[ CI = 510 \]

### Final Answer
The compound interest Divakaran gets after 1 year is **Rs. 510**.

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