Find the compound interest on Rs 125000 for 9 months at 8% per annum, compounded quarterly.

Options

A. 7000
B. 8000
C. 7651
D. 8501

Answer

To find the compound interest on Rs 125,000 for 9 months at an interest rate of 8% per annum, compounded quarterly, we will follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs 125,000
- Rate of interest (R) = 8% per annum
- Time (T) = 9 months

### Step 2: Convert the annual interest rate to a quarterly rate
Since the interest is compounded quarterly, we need to divide the annual rate by 4:
\[ \text{Quarterly Rate} = \frac{R}{4} = \frac{8\%}{4} = 2\% \]

### Step 3: Convert the time period from months to quarters
Since 1 year has 4 quarters and 12 months, we can find the number of quarters in 9 months:
\[ \text{Number of quarters} = \frac{9 \text{ months}}{12 \text{ months/year}} \times 4 \text{ quarters/year} = 3 \text{ quarters} \]

### Step 4: Use the compound interest formula
The formula for the amount \( A \) when compounded quarterly is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( P \) = Principal
- \( r \) = Quarterly interest rate
- \( n \) = Number of quarters

Substituting the values:
\[ A = 125000 \left(1 + \frac{2}{100}\right)^3 \]

### Step 5: Calculate the amount
First, calculate \( 1 + \frac{2}{100} \):
\[ 1 + \frac{2}{100} = 1 + 0.02 = 1.02 \]
Now calculate \( (1.02)^3 \):
\[ (1.02)^3 = 1.061208 \]
Now substitute back to find \( A \):
\[ A = 125000 \times 1.061208 \approx 132651 \]

### Step 6: Calculate the compound interest
The compound interest (CI) is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 132651 - 125000 = 7651 \]

### Final Answer
The compound interest on Rs 125,000 for 9 months at 8% per annum, compounded quarterly, is **Rs 7651**.

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