What is the sum (in Rs) of money which will become Rs 26620 at the rate of 10% per annum at compound interest in three years?

Options

A. 20000
B. 22000
C. 25000
D. 26000

Answer

To find the sum of money (the principal) that will become Rs 26620 at a rate of 10% per annum compounded annually over three years, we can use the formula for compound interest.

### Step-by-Step Solution:

1. **Understand the Formula**:
The formula for the amount \( A \) in compound interest is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
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, we have:
- \( A = 26620 \)
- \( R = 10\% \)
- \( T = 3 \) years

3. **Substitute the Values into the Formula**:
Plugging the known values into the formula:
\[ 26620 = P \left(1 + \frac{10}{100}\right)^3 \]

4. **Simplify the Equation**:
First, simplify \( 1 + \frac{10}{100} \):
\[ 1 + \frac{10}{100} = 1 + 0.1 = 1.1 \]
Now, substitute this back into the equation:
\[ 26620 = P \cdot (1.1)^3 \]

5. **Calculate \( (1.1)^3 \)**:
Calculate \( (1.1)^3 \):
\[ (1.1)^3 = 1.1 \times 1.1 \times 1.1 = 1.331 \]
So, we have:
\[ 26620 = P \cdot 1.331 \]

6. **Solve for \( P \)**:
To find \( P \), rearrange the equation:
\[ P = \frac{26620}{1.331} \]
Now, perform the division:
\[ P \approx 20000 \]

7. **Conclusion**:
Therefore, the sum of money (the principal) is approximately Rs 20000.