The maturity values of a certain sum after two years at 20 % p.a. interest compounded annually is Rs. 14,400/ Find the principal amount.
A. Rs. 9,000
B. Rs, 9,500
C. Rs, 10,000
D. Rs. 10,500

Options

A. A
B. C
C. D
D. B

Answer

To find the principal amount given the maturity value, interest rate, and time period, we can use the formula for compound interest. Here’s the step-by-step solution:

### Step 1: Write down the formula for compound interest.
The formula for the maturity value (A) when interest is compounded annually is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
where:
- \( A \) = maturity value
- \( P \) = principal amount
- \( r \) = rate of interest per annum
- \( t \) = time in years

### Step 2: Substitute the known values into the formula.
From the problem, we know:
- \( A = 14,400 \)
- \( r = 20\% \)
- \( t = 2 \)

Substituting these values into the formula gives us:
\[ 14,400 = P \left(1 + \frac{20}{100}\right)^2 \]

### Step 3: Simplify the expression inside the parentheses.
Calculate \( 1 + \frac{20}{100} \):
\[ 1 + \frac{20}{100} = 1 + 0.2 = 1.2 \]

### Step 4: Substitute back into the equation.
Now we can rewrite the equation:
\[ 14,400 = P (1.2)^2 \]

### Step 5: Calculate \( (1.2)^2 \).
Calculating \( (1.2)^2 \):
\[ (1.2)^2 = 1.44 \]

### Step 6: Substitute this value back into the equation.
Now we have:
\[ 14,400 = P \times 1.44 \]

### Step 7: Solve for \( P \).
To find \( P \), divide both sides by 1.44:
\[ P = \frac{14,400}{1.44} \]

### Step 8: Perform the division.
Calculating the division:
\[ P = 10,000 \]

### Conclusion:
The principal amount is Rs. 10,000.