Mrs. Mathew opened a Recurring Deposit Account in a certain bank and deposited `₹ 640` per month for `4(1)/(2)` years. Find the maturity value of this account. If the bank pays interest at the rate of `12%` per year.

Answer

To find the maturity value of Mrs. Mathew's Recurring Deposit Account, we will follow these steps:

### Step 1: Identify the Monthly Deposit and Duration
- Monthly deposit (P) = ₹640
- Duration = 4.5 years

### Step 2: Convert Duration to Months
- 4.5 years = 4 years + 0.5 years = 4 × 12 + 6 = 54 months

### Step 3: Calculate the Total Principal Amount
- Total Principal Amount (A) = Monthly Deposit × Number of Months
- A = ₹640 × 54 = ₹34,560

### Step 4: Calculate the Interest
- The formula for calculating the interest on a Recurring Deposit is:

\[ \text{Interest} = \frac{P \times n \times (n + 1) \times r}{2400} \]

where:
- P = Monthly deposit = ₹640
- n = Number of months = 54
- r = Rate of interest = 12%

- Substituting the values:

\[ \text{Interest} = \frac{640 \times 54 \times (54 + 1) \times 12}{2400} \]

- Calculate \(n + 1\):
- \(54 + 1 = 55\)

- Now substitute:

\[ \text{Interest} = \frac{640 \times 54 \times 55 \times 12}{2400} \]

### Step 5: Simplify the Calculation
- First, calculate \(640 \times 54 \times 55 \times 12\):
- \(640 \times 54 = 34,560\)
- \(34,560 \times 55 = 1,900,800\)
- \(1,900,800 \times 12 = 22,809,600\)

- Now divide by 2400:

\[ \text{Interest} = \frac{22,809,600}{2400} = 9,504 \]

### Step 6: Calculate the Maturity Value
- Maturity Value = Principal Amount + Interest
- Maturity Value = ₹34,560 + ₹9,504 = ₹44,064

Thus, the maturity value of Mrs. Mathew's Recurring Deposit Account is **₹44,064**.

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