Calculate the compound interest on Rs. 5000 compounded annually for 2 yr and 6 months at the of 1 0% per annum.

Options

A. ₹ 1252.50
B. ₹ 1352.50
C. ₹ 1351.50
D. ₹ 1355.50

Answer

To calculate the compound interest on Rs. 5000 compounded annually for 2 years and 6 months at an interest rate of 10% per annum, follow these steps:

### Step 1: Understand the Given Values
- Principal (P) = Rs. 5000
- Rate of Interest (r) = 10% per annum
- Time (t) = 2 years and 6 months = 2.5 years

### Step 2: Split the Time Period
Since the time is given in two parts (2 years and 6 months), we will calculate the compound interest in two stages:
1. For the first 2 years.
2. For the next 6 months.

### Step 3: Calculate the Amount for the First 2 Years
Using the compound interest formula:
\[ A = P \left(1 + \frac{r}{100}\right)^{n \cdot t} \]
Here, for the first 2 years:
- P = 5000
- r = 10%
- n = 1 (compounded annually)
- t = 2 years

Substituting the values:
\[ A_1 = 5000 \left(1 + \frac{10}{100}\right)^{1 \cdot 2} \]
\[ A_1 = 5000 \left(1 + 0.1\right)^{2} \]
\[ A_1 = 5000 \times (1.1)^{2} \]
\[ A_1 = 5000 \times 1.21 = 6050 \]

### Step 4: Calculate the Amount for the Next 6 Months
Now, we will use the amount from the first part as the principal for the next period:
- New Principal (P) = A_1 = 6050
- r = 10%
- n = 2 (since we are compounding semi-annually for 6 months)
- t = 0.5 years

Using the formula again:
\[ A_2 = 6050 \left(1 + \frac{10}{100 \cdot 2}\right)^{2 \cdot 0.5} \]
\[ A_2 = 6050 \left(1 + \frac{10}{200}\right)^{1} \]
\[ A_2 = 6050 \left(1 + 0.05\right) \]
\[ A_2 = 6050 \times 1.05 = 6352.50 \]

### Step 5: Calculate the Compound Interest
Now, we can find the compound interest by subtracting the principal from the final amount:
\[ \text{Compound Interest} = A_2 - P \]
\[ \text{Compound Interest} = 6352.50 - 5000 = 1352.50 \]

### Final Answer
The compound interest on Rs. 5000 compounded annually for 2 years and 6 months at the rate of 10% per annum is **Rs. 1352.50**.

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