Ritu has a Recurring Deposit Account in a bank and deposits `₹ 80` per month for `18` months. Find the rate of interest paid by the bank if the maturity value of this account is `₹ 1,554`.

Answer

To find the rate of interest paid by the bank on Ritu's Recurring Deposit Account, we will follow these steps:

### Step 1: Identify the Monthly Deposit and Duration
- Monthly Deposit (P) = ₹ 80
- Duration (n) = 18 months

### Step 2: Calculate the Total Principal Amount
The total principal amount (Principal) can be calculated using the formula:
\[ \text{Principal} = \text{Monthly Deposit} \times \text{Duration} \]
\[ \text{Principal} = 80 \times 18 = ₹ 1440 \]

### Step 3: Identify the Maturity Value
The maturity value (Maturity Value) is given as ₹ 1554.

### Step 4: Calculate the Total Interest Earned
The total interest earned can be calculated by subtracting the principal from the maturity value:
\[ \text{Interest} = \text{Maturity Value} - \text{Principal} \]
\[ \text{Interest} = 1554 - 1440 = ₹ 114 \]

### Step 5: Use the Simple Interest Formula
The formula for calculating simple interest is:
\[ \text{Interest} = \frac{P \times n \times (n + 1) \times R}{2400} \]
Where:
- P = Monthly Deposit
- n = Duration in months
- R = Rate of interest

Plugging in the values:
\[ 114 = \frac{80 \times 18 \times 19 \times R}{2400} \]

### Step 6: Rearranging to Find R
Now we will rearrange the equation to solve for R:
\[ R = \frac{114 \times 2400}{80 \times 18 \times 19} \]

### Step 7: Calculate R
Calculating the values step by step:
1. Calculate \( 80 \times 18 \times 19 \):
\[ 80 \times 18 = 1440 \]
\[ 1440 \times 19 = 27360 \]

2. Now substitute back into the equation for R:
\[ R = \frac{114 \times 2400}{27360} \]

3. Calculate \( 114 \times 2400 \):
\[ 114 \times 2400 = 273600 \]

4. Finally, divide:
\[ R = \frac{273600}{27360} = 10 \]

### Conclusion
The rate of interest (R) paid by the bank is **10%**.

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