Find the compound interest on Rs. 12500 at 8% per annum for 9 months compounded quarterly.

Options

A. Rs. 1020
B. Rs. 1428
C. Rs. 510
D. None of these

Answer

To find the compound interest on Rs. 12,500 at 8% per annum for 9 months compounded quarterly, we will follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 12,500
- Rate of interest (R) = 8% per annum
- Time (T) = 9 months = 9/12 years = 0.75 years
- Compounding frequency (n) = Quarterly = 4 times a year

### Step 2: Convert the annual interest rate to the quarterly interest rate
The quarterly interest rate (r) can be calculated as follows:
\[ r = \frac{R}{n} = \frac{8\%}{4} = 2\% \]

### Step 3: Calculate the total number of compounding periods
The total number of compounding periods (N) for 9 months is:
\[ N = n \times T = 4 \times 0.75 = 3 \]

### Step 4: Use the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^N \]
Where:
- A = Amount after N compounding periods
- P = Principal
- r = Quarterly interest rate
- N = Total number of compounding periods

Substituting the values into the formula:
\[ A = 12500 \left(1 + \frac{2}{100}\right)^3 \]

### Step 5: Calculate the amount (A)
First, calculate \( \left(1 + \frac{2}{100}\right) \):
\[ \left(1 + \frac{2}{100}\right) = 1 + 0.02 = 1.02 \]

Now raise it to the power of 3:
\[ (1.02)^3 = 1.061208 \]

Now calculate the amount (A):
\[ A = 12500 \times 1.061208 = 13265.10 \]

### Step 6: Calculate the compound interest (CI)
The compound interest (CI) is calculated as:
\[ CI = A - P \]
\[ CI = 13265.10 - 12500 = 765.10 \]

### Final Answer
The compound interest on Rs. 12,500 at 8% per annum for 9 months compounded quarterly is **Rs. 765.10**.