Katrina opened a recurring deposit account with a Nationalised Bank for a period of 2 years. If the bank pays interest at the rate of 6% per annum and the monthly instalment is Rs 1,000, find the :
(ii) maturity value.

Answer

To find the maturity value of Katrina's recurring deposit account, we will follow these steps:

### Step 1: Identify the given values
- Monthly installment (P) = Rs 1,000
- Total period (n) = 2 years = 24 months
- Rate of interest (R) = 6% per annum

### Step 2: Calculate the total amount deposited
The total amount deposited over the 2 years can be calculated as:
\[ \text{Total Deposited} = \text{Monthly Installment} \times \text{Number of Months} = P \times n \]
Substituting the values:
\[ \text{Total Deposited} = 1000 \times 24 = 24000 \text{ Rs} \]

### Step 3: Calculate the interest earned
The formula for calculating the interest on a recurring deposit is:
\[ \text{Interest} = P \times n \times \frac{n + 1}{2} \times \frac{R}{12 \times 100} \]
Substituting the values:
\[ \text{Interest} = 1000 \times 24 \times \frac{24 + 1}{2} \times \frac{6}{12 \times 100} \]
Calculating step-by-step:
1. Calculate \(n + 1 = 24 + 1 = 25\)
2. Calculate \(\frac{25}{2} = 12.5\)
3. Calculate \(\frac{6}{12 \times 100} = \frac{6}{1200} = 0.005\)
4. Now substitute back:
\[ \text{Interest} = 1000 \times 24 \times 12.5 \times 0.005 \]
5. Calculate \(1000 \times 24 = 24000\)
6. Calculate \(24000 \times 12.5 = 300000\)
7. Finally, calculate \(300000 \times 0.005 = 1500\)

Thus, the interest earned is Rs 1,500.

### Step 4: Calculate the maturity value
The maturity value is the sum of the total amount deposited and the interest earned:
\[ \text{Maturity Value} = \text{Total Deposited} + \text{Interest} \]
Substituting the values:
\[ \text{Maturity Value} = 24000 + 1500 = 25500 \text{ Rs} \]

### Final Answer
The maturity value of Katrina's recurring deposit account is Rs 25,500.

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