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

Options

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

Answer

To find the amount invested (P) in the fixed deposit scheme, we can follow these steps:

### Step 1: Understand the Interest Rates
The bank offers:
- 8% interest for the first year
- 9% interest for the second year

### Step 2: Set Up the Equation
The total amount received after 2 years is ₹ 17,658. The amount can be calculated using the formula for compound interest:

\[ A = P \times (1 + r_1) \times (1 + r_2) \]

Where:
- \( A \) = total amount received after 2 years (₹ 17,658)
- \( P \) = principal amount (the amount invested)
- \( r_1 \) = interest rate for the first year (8% or 0.08)
- \( r_2 \) = interest rate for the second year (9% or 0.09)

### Step 3: Substitute the Values
Substituting the values into the equation:

\[ 17,658 = P \times (1 + 0.08) \times (1 + 0.09) \]

This simplifies to:

\[ 17,658 = P \times (1.08) \times (1.09) \]

### Step 4: Calculate the Multiplication
Now calculate \( 1.08 \times 1.09 \):

\[ 1.08 \times 1.09 = 1.1762 \]

### Step 5: Rewrite the Equation
Now we can rewrite the equation as:

\[ 17,658 = P \times 1.1762 \]

### Step 6: Solve for P
To find \( P \), divide both sides by 1.1762:

\[ P = \frac{17,658}{1.1762} \]

### Step 7: Calculate P
Now perform the division:

\[ P \approx 15,000 \]

### Conclusion
The amount invested (P) is approximately ₹ 15,000.

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