Rekha opened a recurring deposite account for 20 months. The rate of interest is 9% per annum and Rekha receives Rs 441 as interest at the time of maturity.
Find the amount Rekha deposited each month.

Answer

To find the amount Rekha deposited each month in her recurring deposit account, we can follow these steps:

### Step 1: Understand the formula for interest in a recurring deposit
The formula for calculating the interest earned on a recurring deposit is given by:
\[ I = \frac{P \times r \times n(n+1)}{2400} \]
where:
- \(I\) = Interest earned
- \(P\) = Amount deposited each month
- \(r\) = Rate of interest per annum
- \(n\) = Number of months

### Step 2: Substitute the known values into the formula
From the problem, we know:
- \(I = 441\) (the interest earned)
- \(r = 9\%\) (the rate of interest)
- \(n = 20\) (the number of months)

Substituting these values into the formula:
\[ 441 = \frac{P \times 9 \times 20 \times 21}{2400} \]

### Step 3: Simplify the equation
First, we can multiply both sides by 2400 to eliminate the fraction:
\[ 441 \times 2400 = P \times 9 \times 20 \times 21 \]

Calculating the left side:
\[ 441 \times 2400 = 1058400 \]

Now we have:
\[ 1058400 = P \times 9 \times 20 \times 21 \]

### Step 4: Calculate \(9 \times 20 \times 21\)
Calculating the right side:
\[ 9 \times 20 = 180 \]
\[ 180 \times 21 = 3780 \]

So, we can rewrite the equation as:
\[ 1058400 = P \times 3780 \]

### Step 5: Solve for \(P\)
Now, divide both sides by 3780 to find \(P\):
\[ P = \frac{1058400}{3780} \]

Calculating \(P\):
\[ P = 280 \]

### Conclusion
Thus, the amount Rekha deposited each month is **Rs 280**.

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