A certain bank offers `8%` rate of Interest on the 1st year and `9%` on the 2nd year in a certain fixed deposit scheme. If `Rs. 17,658` are received after investing for 2 years in this scheme, then what was the amount (in Rs.) invested?

Options

A. A) 16000
B. B) 15000
C. C) 15500
D. D) 16500

Answer

To find the amount invested in the fixed deposit scheme, we will use the concept of compound interest. Let's break down the solution step by step.

### Step 1: Understand the interest rates for each year
The bank offers:
- **8% interest for the first year**
- **9% interest for the second year**

### Step 2: Set up the formula for the amount after 2 years
Let the principal amount (the amount invested) be denoted as \( P \).

The amount after the first year can be calculated as:
\[ A_1 = P + \left( \frac{8}{100} \times P \right) = P \left(1 + \frac{8}{100}\right) = P \times 1.08 \]

For the second year, we apply the 9% interest on the amount from the first year:
\[ A_2 = A_1 + \left( \frac{9}{100} \times A_1 \right) = A_1 \left(1 + \frac{9}{100}\right) = A_1 \times 1.09 \]

Substituting \( A_1 \):
\[ A_2 = (P \times 1.08) \times 1.09 = P \times 1.08 \times 1.09 \]

### Step 3: Calculate the total amount after 2 years
Calculating \( 1.08 \times 1.09 \):
\[ 1.08 \times 1.09 = 1.1772 \]
Thus, the amount after 2 years is:
\[ A_2 = P \times 1.1772 \]

### Step 4: Set up the equation with the final amount
According to the problem, the total amount received after 2 years is \( 17,658 \):
\[ P \times 1.1772 = 17,658 \]

### Step 5: Solve for \( P \)
To find \( P \), we rearrange the equation:
\[ P = \frac{17,658}{1.1772} \]

Calculating this gives:
\[ P \approx 15,000 \]

### Conclusion
The amount invested was approximately **Rs. 15,000**.

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