Mr Sridharan invested money in two schemes A and B, offering compound interest at 8 percent per annum and 9 percent per annum respectively. If the total amount of interest accrued through the two schemes together in two years was 4818.30 and the total amount invested was 27,000, what was the amount invested in Scheme A ?

Options

A. 15000
B. 13500
C. 12000
D. Cannot be determined

Answer

To solve the problem step by step, we need to find the amount Mr. Sridharan invested in Scheme A. Let's denote the amount invested in Scheme A as \( x \) and the amount invested in Scheme B as \( 27000 - x \).

### Step 1: Set up the equations for compound interest
The formula for the amount \( A \) after \( n \) years with principal \( P \) and rate \( r \) is given by:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
For Scheme A, the interest rate is 8% and for Scheme B, it is 9%. The total interest accrued from both schemes in 2 years is given as 4818.30.

### Step 2: Calculate the total amount for both schemes
- For Scheme A:
\[ A_A = x \left(1 + \frac{8}{100}\right)^2 = x \left(1.08\right)^2 = x \cdot 1.1664 \]
- For Scheme B:
\[ A_B = (27000 - x) \left(1 + \frac{9}{100}\right)^2 = (27000 - x) \left(1.09\right)^2 = (27000 - x) \cdot 1.1881 \]

### Step 3: Calculate the total interest from both schemes
The total interest from both schemes is:
\[ \text{Total Interest} = A_A - x + A_B - (27000 - x) \]
This simplifies to:
\[ \text{Total Interest} = (x \cdot 1.1664 - x) + ((27000 - x) \cdot 1.1881 - (27000 - x)) \]
\[ = x(1.1664 - 1) + (27000 \cdot 1.1881 - 27000) - x(1.1881 - 1) \]
\[ = x(0.1664) + 27000(0.1881) - x(0.1881) \]
\[ = x(0.1664 - 0.1881) + 27000 \cdot 0.1881 \]
\[ = -0.0217x + 5079.7 \]

### Step 4: Set the equation equal to the total interest
We know the total interest is 4818.30, so we set up the equation:
\[ -0.0217x + 5079.7 = 4818.30 \]

### Step 5: Solve for \( x \)
Rearranging the equation gives:
\[ -0.0217x = 4818.30 - 5079.7 \]
\[ -0.0217x = -261.4 \]
\[ x = \frac{-261.4}{-0.0217} \approx 12000 \]

### Step 6: Conclusion
Thus, the amount invested in Scheme A is \( \boxed{12000} \).