The compound interest on Rs. 16000 for 9 months at 20% per annum, if interest being compounded quarterly, is:

Options

A. (a) Rs 2500
B. (b) Rs 2522
C. (c) Rs 2200
D. (d) Rs 2000

Answer

To solve the problem of finding the compound interest on Rs. 16,000 for 9 months at an interest rate of 20% per annum, compounded quarterly, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Variables**:
- Principal (P) = Rs. 16,000
- Rate of interest (R) = 20% per annum
- Time (T) = 9 months

2. **Convert the Time into Quarters**:
- Since the interest is compounded quarterly, we need to convert the time into quarters.
- 1 year = 12 months, therefore, 9 months = 9/3 = 3 quarters.

3. **Adjust the Rate of Interest**:
- The annual interest rate is 20%, but since it is compounded quarterly, we need to divide this rate by 4 (the number of quarters in a year).
- Quarterly interest rate = 20% / 4 = 5% per quarter.

4. **Use the Compound Interest Formula**:
- The formula for the amount (A) when interest is compounded is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
where \( n \) is the number of compounding periods (quarters).
- Substitute the values into the formula:
\[ A = 16000 \left(1 + \frac{5}{100}\right)^3 \]
\[ A = 16000 \left(1 + 0.05\right)^3 \]
\[ A = 16000 \left(1.05\right)^3 \]

5. **Calculate \( (1.05)^3 \)**:
- First, calculate \( (1.05)^3 \):
\[ (1.05)^3 = 1.157625 \]

6. **Calculate the Amount (A)**:
- Now substitute back to find A:
\[ A = 16000 \times 1.157625 \]
\[ A = 18522 \]

7. **Calculate the Compound Interest (CI)**:
- The formula for compound interest is:
\[ CI = A - P \]
- Substitute the values:
\[ CI = 18522 - 16000 \]
\[ CI = 2522 \]

### Final Answer:
The compound interest on Rs. 16,000 for 9 months at 20% per annum, compounded quarterly, is Rs. 2,522.

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