A invested an amount of x rupees in a bank for 2 years which gave 5% interest in year 1 and 6% interest in year 2. The amount received after 2 years is Rs 24,486. What is the value of x?

Options

A. 23000
B. 22000
C. 22500
D. 21500

Answer

To find the value of \( x \) (the principal amount invested by A), we will use the formula for compound interest with different rates for each year.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Amount after 2 years, \( A = 24,486 \) rupees
- Rate of interest for Year 1, \( R_1 = 5\% = \frac{5}{100} = 0.05 \)
- Rate of interest for Year 2, \( R_2 = 6\% = \frac{6}{100} = 0.06 \)

2. **Use the Compound Interest Formula:**
When the interest rates are different for each year, the formula to calculate the amount is:
\[ A = P \left(1 + R_1\right) \left(1 + R_2\right) \]
Here, \( P \) is the principal amount (which we need to find).

3. **Substituting the Values:**
Substitute \( A \), \( R_1 \), and \( R_2 \) into the formula:
\[ 24,486 = x \left(1 + 0.05\right) \left(1 + 0.06\right) \]
This simplifies to:
\[ 24,486 = x \left(1.05\right) \left(1.06\right) \]

4. **Calculating the Product of the Factors:**
Calculate \( 1.05 \times 1.06 \):
\[ 1.05 \times 1.06 = 1.113 \]
Therefore, we have:
\[ 24,486 = x \times 1.113 \]

5. **Solving for \( x \):**
Rearranging the equation to solve for \( x \):
\[ x = \frac{24,486}{1.113} \]
Now, calculate \( x \):
\[ x \approx 22,000 \]

### Final Result:
The value of \( x \) is approximately **22,000 rupees**.

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