The amount of each instalment will discharge on debit of Rs. 3220 due In 4 yr at 10% simple interest is
(a)Rs. 700
(b)Rs. 1000
(c)Rs. 500
(d)Rs. 900

Options

A. Rs. 700
B. Rs. 1000
C. Rs. 500
D. Rs. 900

Answer

To solve the problem of finding the amount of each installment that will discharge a debit of Rs. 3220 due in 4 years at 10% simple interest, we can follow these steps:

### Step 1: Understand the Problem
We need to find the amount of each installment that will pay off a total debt of Rs. 3220 over 4 years at a simple interest rate of 10%.

### Step 2: Calculate Total Interest
First, we need to calculate the total interest that will be accrued over the 4 years. The formula for simple interest is:

\[ \text{Interest} = \frac{P \times R \times T}{100} \]

Where:
- \( P \) = Principal amount (in this case, Rs. 3220)
- \( R \) = Rate of interest (10%)
- \( T \) = Time (4 years)

Substituting the values:

\[ \text{Interest} = \frac{3220 \times 10 \times 4}{100} = \frac{128800}{100} = 1288 \]

### Step 3: Calculate Total Amount
Now, we can calculate the total amount that needs to be paid after 4 years, which is the sum of the principal and the interest:

\[ \text{Total Amount} = P + \text{Interest} = 3220 + 1288 = 4508 \]

### Step 4: Determine the Number of Installments
Since we are making 4 installments (one each year), we can find the amount of each installment by dividing the total amount by the number of installments:

\[ \text{Installment Amount} = \frac{\text{Total Amount}}{4} = \frac{4508}{4} = 1127 \]

### Step 5: Verify the Options
Now, we need to check the options given in the question to find the closest installment amount. The options are:
(a) Rs. 700
(b) Rs. 1000
(c) Rs. 500
(d) Rs. 900

Since our calculated installment amount (Rs. 1127) does not match any of the options, we need to reassess our approach.

### Step 6: Reassess the Installment Calculation
We need to consider the timing of each installment. The first installment is paid 3 years before the due date, the second 2 years before, the third 1 year before, and the fourth on the due date.

Let’s denote the installment amount as \( x \).

1. The first installment will have 3 years of interest.
2. The second installment will have 2 years of interest.
3. The third installment will have 1 year of interest.
4. The fourth installment will have 0 years of interest.

The total interest for each installment can be calculated as follows:

\[ \text{Total Interest} = \left(3x \cdot \frac{10}{100}\right) + \left(2x \cdot \frac{10}{100}\right) + \left(1x \cdot \frac{10}{100}\right) + 0 \]

This simplifies to:

\[ \text{Total Interest} = \frac{30x}{100} = 0.3x \]

### Step 7: Set Up the Equation
Now, we can set up the equation to find \( x \):

\[ x + x + x + x + 0.3x = 3220 \]

This simplifies to:

\[ 4x + 0.3x = 3220 \]
\[ 4.3x = 3220 \]

### Step 8: Solve for \( x \)
Now, we can solve for \( x \):

\[ x = \frac{3220}{4.3} \approx 748.84 \]

### Step 9: Conclusion
The closest option to Rs. 748.84 is Rs. 700.

Thus, the amount of each installment will discharge the debit of Rs. 3220 due in 4 years at 10% simple interest is **(a) Rs. 700**.

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