The monthly instalment of a recurring deposit account is Rs 2,400. If the account is held for 1 year 6 months and its maturity value is Rs 47,304, find the rate of interest.

Answer

To find the rate of interest for the recurring deposit account, we can follow these steps:

### Step 1: Calculate the total amount deposited
The monthly installment is Rs 2,400, and the account is held for 1 year and 6 months, which is equal to 18 months.

\[ \text{Total Amount Deposited} = \text{Monthly Installment} \times \text{Number of Months} \]
\[ \text{Total Amount Deposited} = 2400 \times 18 = 43200 \text{ Rs} \]

### Step 2: Calculate the total interest earned
The maturity value of the account is given as Rs 47,304. To find the interest earned, we subtract the total amount deposited from the maturity value.

\[ \text{Interest} = \text{Maturity Value} - \text{Total Amount Deposited} \]
\[ \text{Interest} = 47304 - 43200 = 4104 \text{ Rs} \]

### Step 3: Calculate the total principal for interest calculation
The principal for calculating interest in a recurring deposit account is calculated using the formula:

\[ \text{Principal} = \text{Monthly Installment} \times \text{Number of Months} \times \left(\frac{\text{Number of Months} + 1}{2}\right) \]
\[ \text{Principal} = 2400 \times 18 \times \left(\frac{18 + 1}{2}\right) = 2400 \times 18 \times 9.5 = 410400 \text{ Rs} \]

### Step 4: Calculate the rate of interest
Using the formula for simple interest, we can find the rate of interest (R):

\[ \text{Interest} = \frac{\text{Principal} \times R \times T}{100} \]
Where:
- Interest = 4104 Rs
- Principal = 410400 Rs
- Time (T) = 18 months = 1.5 years

Rearranging the formula to solve for R:

\[ R = \frac{\text{Interest} \times 100}{\text{Principal} \times T} \]
Substituting the values:

\[ R = \frac{4104 \times 100}{410400 \times 1.5} \]
\[ R = \frac{410400}{615600} = 0.6667 \times 100 = 12 \text{ percent} \]

### Final Answer:
The rate of interest is **12%**.

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