K borrowed Rs. P at a compound interest of 20% p.a. for 2 years . Interest amount payable was Rs 5,280. What was the value of P ?

Options

A. Rs 12,000
B. Rs 11,000
C. Rs 11,750
D. Rs 12,500

Answer

To find the principal amount \( P \) that K borrowed at a compound interest rate of 20% per annum for 2 years, we can use the formula for compound interest:

\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]

Where:
- \( CI \) is the compound interest,
- \( P \) is the principal amount,
- \( R \) is the rate of interest,
- \( T \) is the time in years.

Given:
- \( CI = 5280 \)
- \( R = 20\% \)
- \( T = 2 \) years

### Step 1: Substitute the values into the compound interest formula

\[ 5280 = P \left(1 + \frac{20}{100}\right)^2 - P \]

### Step 2: Simplify the expression inside the parentheses

\[ 1 + \frac{20}{100} = 1 + 0.2 = 1.2 \]

### Step 3: Raise the result to the power of 2

\[ (1.2)^2 = 1.44 \]

### Step 4: Substitute back into the equation

\[ 5280 = P(1.44) - P \]

### Step 5: Factor out \( P \)

\[ 5280 = P(1.44 - 1) \]
\[ 5280 = P(0.44) \]

### Step 6: Solve for \( P \)

\[ P = \frac{5280}{0.44} \]

### Step 7: Calculate the value of \( P \)

To simplify \( \frac{5280}{0.44} \), we can multiply both the numerator and the denominator by 100 to eliminate the decimal:

\[ P = \frac{5280 \times 100}{44} = \frac{528000}{44} \]

Now, divide:

\[ P = 12000 \]

Thus, the principal amount \( P \) is Rs. 12,000.

### Final Answer
The value of \( P \) is Rs. 12,000.

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