The sum for 2 years gives a compound interest of `Rs. 3225` at the rate of `15%` per annum. The sum is

Options

A. `Rs. 10000 `
B. `Rs. 20000 `
C. `Rs. 15000 `
D. `Rs. 32250`

Answer

To find the principal sum (P) that gives a compound interest of Rs. 3225 at a rate of 15% per annum for 2 years, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Compound Interest**:
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
where:
- \( A \) = Amount after time \( t \)
- \( P \) = Principal amount (initial sum)
- \( r \) = Rate of interest per annum
- \( t \) = Time in years

2. **Identify the Given Values**:
From the question:
- Compound Interest (CI) = Rs. 3225
- Rate (r) = 15%
- Time (t) = 2 years

3. **Relate Compound Interest to Amount**:
The compound interest can also be expressed as:
\[ CI = A - P \]
Therefore, we can express the amount \( A \) as:
\[ A = P + CI \]
Substituting the value of CI:
\[ A = P + 3225 \]

4. **Substitute the Amount in the Compound Interest Formula**:
Substitute \( A \) in the compound interest formula:
\[ P + 3225 = P \left(1 + \frac{15}{100}\right)^2 \]
Simplifying the right side:
\[ P + 3225 = P \left(1 + 0.15\right)^2 = P \left(1.15\right)^2 \]
Calculate \( (1.15)^2 \):
\[ (1.15)^2 = 1.3225 \]
Therefore, we have:
\[ P + 3225 = 1.3225P \]

5. **Rearranging the Equation**:
Rearranging gives:
\[ 1.3225P - P = 3225 \]
Simplifying:
\[ 0.3225P = 3225 \]

6. **Solve for Principal (P)**:
Divide both sides by 0.3225:
\[ P = \frac{3225}{0.3225} \]
Calculating the right side:
\[ P = 10000 \]

### Final Answer:
The principal sum is **Rs. 10,000**.

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