If a sum of Rs.12500 is Invested for 1 year at 12% per annum interest being compounded semiannually, then interest earned is :

Options

A. `Rs.1505`
B. `Rs.1535`
C. `Rs. 1545`
D. `Rs. 1550`

Answer

To solve the problem of calculating the compound interest earned on an investment of Rs. 12,500 at an interest rate of 12% per annum compounded semiannually, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 12,500
- Rate of interest (R) = 12% per annum
- Time (T) = 1 year

### Step 2: Adjust the interest rate and time for semiannual compounding
Since the interest is compounded semiannually, we need to adjust the rate and the time:
- The number of compounding periods in 1 year = 2 (since it is compounded semiannually)
- Therefore, the effective rate per period = R / 2 = 12% / 2 = 6%
- The total number of compounding periods = 2 (for 1 year)

### Step 3: Use the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- A = the amount after n periods
- P = principal amount
- r = rate of interest per period
- n = number of compounding periods

Substituting the values:
\[ A = 12500 \left(1 + \frac{6}{100}\right)^2 \]
\[ A = 12500 \left(1 + 0.06\right)^2 \]
\[ A = 12500 \left(1.06\right)^2 \]

### Step 4: Calculate \( (1.06)^2 \)
Calculating \( (1.06)^2 \):
\[ (1.06)^2 = 1.1236 \]

### Step 5: Calculate the total amount (A)
Now substitute back into the formula:
\[ A = 12500 \times 1.1236 \]
\[ A = 14029.50 \]

### Step 6: Calculate the compound interest (CI)
To find the compound interest earned, subtract the principal from the total amount:
\[ CI = A - P \]
\[ CI = 14029.50 - 12500 \]
\[ CI = 1529.50 \]

### Final Answer
The interest earned is Rs. 1529.50.

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