Mrs. Geeta deposited `₹ 350` per month in a bank for `1` year and `3` months under the Recurring Deposit Scheme. If the maturity value of her deposits is `₹ 5,565`, Find the rate of interest per annum.

Answer

To find the rate of interest per annum for Mrs. Geeta's recurring deposit, we can follow these steps:

### Step 1: Identify the given values
- Monthly deposit (P) = ₹350
- Total duration = 1 year and 3 months = 15 months
- Maturity value (M) = ₹5,565

### Step 2: Calculate the total principal amount deposited
The total principal amount (A) deposited over 15 months is:
\[ A = P \times \text{number of months} = 350 \times 15 = ₹5,250 \]

### Step 3: Use the formula for Simple Interest (SI) in Recurring Deposits
The formula for Simple Interest in a recurring deposit scheme is:
\[ SI = \frac{P \times n \times (n - 1)}{2 \times 12} \times \frac{r}{100} \]
Where:
- \( n \) = total number of months = 15
- \( r \) = rate of interest per annum (which we need to find)

### Step 4: Substitute the values into the SI formula
Substituting the values into the formula:
\[ SI = \frac{350 \times 15 \times (15 - 1)}{2 \times 12} \times \frac{r}{100} \]
Calculating \( (15 - 1) \):
\[ SI = \frac{350 \times 15 \times 14}{2 \times 12} \times \frac{r}{100} \]

### Step 5: Simplify the expression
Calculating the numerator:
\[ SI = \frac{350 \times 15 \times 14}{24} \times \frac{r}{100} \]
Calculating \( 350 \times 15 = 5250 \):
\[ SI = \frac{5250 \times 14}{24} \times \frac{r}{100} \]
Calculating \( 5250 \times 14 = 73500 \):
\[ SI = \frac{73500}{24} \times \frac{r}{100} \]
Calculating \( \frac{73500}{24} = 3062.5 \):
\[ SI = 3062.5 \times \frac{r}{100} \]

### Step 6: Relate SI to the maturity value
The maturity value (M) is given by:
\[ M = A + SI \]
So, substituting the values:
\[ 5565 = 5250 + SI \]
This gives:
\[ SI = 5565 - 5250 = 315 \]

### Step 7: Set the equations equal to each other
Now we have:
\[ 3062.5 \times \frac{r}{100} = 315 \]

### Step 8: Solve for r
To find \( r \):
\[ r = \frac{315 \times 100}{3062.5} \]
Calculating:
\[ r = \frac{31500}{3062.5} \approx 10.26 \]

### Step 9: Convert to percentage
Since \( r \) is in terms of percentage, we can round it to:
\[ r \approx 10.26\% \]

### Final Answer
The rate of interest per annum is approximately **10.26%**.

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