An investor invested his saving in the stock market. The value of his investments increased by 12% and 9% in the first year and the second year respectively. If the value of his investments after two years became Rs 97,664 then how much had he invested (in Rs)?

Options

A. 81000
B. 75000
C. 80000
D. 72000

Answer

To find out how much the investor initially invested, we can use the concept of compound interest. Here’s the step-by-step solution:

### Step 1: Define the initial investment
Let the initial investment be Rs X.

### Step 2: Calculate the value after the first year
The investment increases by 12% in the first year. Therefore, the value after the first year can be calculated as:
\[ \text{Value after 1st year} = X + (12\% \text{ of } X) = X \times \left(1 + \frac{12}{100}\right) = X \times \frac{112}{100} = X \times 1.12 \]

### Step 3: Calculate the value after the second year
In the second year, the investment increases by 9%. Thus, the value after the second year can be calculated as:
\[ \text{Value after 2nd year} = \text{Value after 1st year} + (9\% \text{ of Value after 1st year}) = (X \times 1.12) \times \left(1 + \frac{9}{100}\right) = (X \times 1.12) \times \frac{109}{100} \]

### Step 4: Set up the equation
According to the problem, the value of the investment after 2 years is Rs 97,664. Therefore, we can set up the equation:
\[ (X \times 1.12) \times \frac{109}{100} = 97,664 \]

### Step 5: Simplify the equation
Now, we can simplify the left side:
\[ X \times 1.12 \times 1.09 = 97,664 \]
Calculating \(1.12 \times 1.09\):
\[ 1.12 \times 1.09 = 1.2208 \]
So, we have:
\[ X \times 1.2208 = 97,664 \]

### Step 6: Solve for X
To find X, divide both sides by 1.2208:
\[ X = \frac{97,664}{1.2208} \]
Calculating the right side:
\[ X = 80,000 \]

### Conclusion
The initial investment made by the investor is Rs 80,000.

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