After 3 years Rs 9,270 was paid in 3 annual in stallments in 3 years. If the rate of simple interest is 3% per annum, find out the amount of each installment.

Options

A. 2000
B. 1500
C. 2300
D. 3000

Answer

To solve the problem of finding the amount of each installment when Rs 9,270 is paid in 3 annual installments over 3 years at a simple interest rate of 3% per annum, we can follow these steps:

### Step 1: Understand the Total Amount and Interest
The total amount paid after 3 years is Rs 9,270. This amount includes the principal and the interest accrued over the period.

### Step 2: Calculate the Total Interest
The formula for simple interest is:
\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

In this case, we need to find the total interest for the 3 installments over 3 years.

### Step 3: Set Up the Equation for Installments
Let the amount of each installment be \( A \). Since there are 3 installments, the total amount paid can be expressed as:
\[ A_1 + A_2 + A_3 = 9270 \]
Where:
- \( A_1 \) is the first installment (paid at the end of year 1),
- \( A_2 \) is the second installment (paid at the end of year 2),
- \( A_3 \) is the third installment (paid at the end of year 3).

### Step 4: Calculate the Interest for Each Installment
The interest for each installment can be calculated as follows:
- For \( A_1 \): Interest for 2 years (since it is paid at the end of the first year)
\[ \text{Interest}_1 = \frac{A \times 3 \times 2}{100} = \frac{6A}{100} = 0.06A \]
- For \( A_2 \): Interest for 1 year (paid at the end of the second year)
\[ \text{Interest}_2 = \frac{A \times 3 \times 1}{100} = \frac{3A}{100} = 0.03A \]
- For \( A_3 \): No interest (since it is paid at the end of the third year)
\[ \text{Interest}_3 = 0 \]

### Step 5: Write the Total Amount Equation
The total amount paid after including interest is:
\[ A + (A + 0.06A) + (A + 0.03A) = 9270 \]
This simplifies to:
\[ A + A + 0.06A + A + 0.03A = 9270 \]
\[ 3.09A = 9270 \]

### Step 6: Solve for \( A \)
Now, divide both sides by 3.09 to find the amount of each installment:
\[ A = \frac{9270}{3.09} \approx 3000 \]

### Conclusion
The amount of each installment is approximately Rs 3,000.

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