Manish opens a Recurring Deposit Account with the bank of Rajasthan and deposits `₹ 600` per month for `20` months . Calculate the maturity value of this account, if the bank pays interest at the rate of `10%` per annum.

Answer

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

### Step 1: Calculate the Total Principal
Manish deposits ₹600 per month for 20 months.
\[ \text{Total Principal} = \text{Monthly Deposit} \times \text{Number of Months} = 600 \times 20 = ₹12,000 \]

### Step 2: Calculate the Interest
The formula for calculating interest on a Recurring Deposit is:
\[ \text{Interest} = \frac{P \times n \times (n + 1) \times r}{2400} \]
Where:
- \( P \) = Monthly Deposit
- \( n \) = Number of Months
- \( r \) = Rate of Interest (in percentage)

Substituting the values:
- \( P = 600 \)
- \( n = 20 \)
- \( r = 10 \)

Now plug these values into the formula:
\[ \text{Interest} = \frac{600 \times 20 \times (20 + 1) \times 10}{2400} \]
Calculating \( n + 1 \):
\[ n + 1 = 20 + 1 = 21 \]
Now substituting this back into the formula:
\[ \text{Interest} = \frac{600 \times 20 \times 21 \times 10}{2400} \]

### Step 3: Simplify the Calculation
Calculating the numerator:
\[ 600 \times 20 = 12000 \]
\[ 12000 \times 21 = 252000 \]
\[ 252000 \times 10 = 2520000 \]
Now divide by 2400:
\[ \text{Interest} = \frac{2520000}{2400} = ₹1050 \]

### Step 4: Calculate the Maturity Value
The maturity value is the total principal plus the interest earned:
\[ \text{Maturity Value} = \text{Total Principal} + \text{Interest} = 12000 + 1050 = ₹13050 \]

### Final Answer
The maturity value of Manish's Recurring Deposit Account is **₹13,050**.

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