A man deposits Rs 900 per month in a recurring account for 2 years. If he gets Rs 1,800 as interest at the time of maturity, find the rate of interest.

Answer

To find the rate of interest in this problem, we will use the formula for simple interest in a recurring deposit account. Here's the step-by-step solution:

### Step 1: Identify the given values
- Monthly deposit (P) = Rs 900
- Total time (T) = 2 years = 2 × 12 months = 24 months
- Total interest (SI) = Rs 1800

### Step 2: Calculate the total principal amount
The total principal (A) deposited over 24 months can be calculated as:
\[ A = P \times n \]
Where \( n \) is the number of months.
\[ A = 900 \times 24 = 21600 \text{ Rs} \]

### Step 3: Use the formula for simple interest
The formula for simple interest is:
\[ SI = \frac{P \times n \times (n + 1)}{2 \times 12} \times \frac{R}{100} \]
Where:
- \( SI \) = Simple Interest
- \( P \) = Monthly deposit
- \( n \) = Total number of months
- \( R \) = Rate of interest

### Step 4: Substitute the known values into the formula
We need to find \( R \), so we rearrange the formula:
\[ 1800 = \frac{900 \times 24 \times 25}{2 \times 12} \times \frac{R}{100} \]

### Step 5: Simplify the equation
First, calculate \( \frac{900 \times 24 \times 25}{2 \times 12} \):
- \( 2 \times 12 = 24 \)
- Therefore, \( \frac{900 \times 24 \times 25}{24} = 900 \times 25 = 22500 \)

Now, we can rewrite the equation:
\[ 1800 = 22500 \times \frac{R}{100} \]

### Step 6: Solve for \( R \)
Multiply both sides by 100:
\[ 1800 \times 100 = 22500R \]
\[ 180000 = 22500R \]
Now, divide both sides by 22500:
\[ R = \frac{180000}{22500} = 8 \]

### Final Answer
The rate of interest \( R \) is **8%**.

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