Pramod deposits `₹ 600` per month in a Recurring Deposit Account for `4` years. If the rate of interest is `8%` per year, calculate the maturity value of his account.

Answer

To calculate the maturity value of Pramod's Recurring Deposit Account, we will follow these steps:

### Step 1: Identify the given values
- Monthly deposit (P) = ₹600
- Rate of interest (R) = 8% per annum
- Duration (T) = 4 years

### Step 2: Convert the duration into months
Since the deposits are made monthly, we need to convert the duration from years to months:
- Duration in months (n) = 4 years × 12 months/year = 48 months

### Step 3: Calculate the principal amount
The principal amount (Total amount deposited) is calculated as:
\[ \text{Principal Amount} = \text{Monthly Deposit} \times \text{Number of Months} \]
\[ \text{Principal Amount} = 600 \times 48 = ₹28,800 \]

### Step 4: Calculate the interest amount
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
- n = Total number of months
- R = Rate of interest per annum

Substituting the values:
\[ \text{Interest} = \frac{600 \times 48 \times (48 + 1) \times 8}{2400} \]
\[ \text{Interest} = \frac{600 \times 48 \times 49 \times 8}{2400} \]

### Step 5: Simplify the interest calculation
First, calculate the numerator:
- \( 600 \times 48 = 28,800 \)
- \( 28,800 \times 49 = 1,411,200 \)
- \( 1,411,200 \times 8 = 11,289,600 \)

Now divide by 2400:
\[ \text{Interest} = \frac{11,289,600}{2400} = ₹4,704 \]

### Step 6: Calculate the maturity value
The maturity value (M) is the sum of the principal amount and the interest amount:
\[ \text{Maturity Value} = \text{Principal Amount} + \text{Interest} \]
\[ \text{Maturity Value} = 28,800 + 4,704 = ₹33,504 \]

### Final Answer
The maturity value of Pramod's account after 4 years is **₹33,504**.

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