Amit deposited `₹ 150` per month in a bank for `8` months under the Recurring Deposit Scheme. What will be the maturity value of his deposits, if the rate of interest is `8%` per annum and interest is calculated at the end of every month ?

Answer

To find the maturity value of Amit's deposits under the Recurring Deposit Scheme, we will follow these steps:

### Step 1: Calculate the Total Principal Amount
Amit deposits ₹150 per month for 8 months. Therefore, the total principal amount (P) can be calculated as:
\[ P = \text{Monthly Deposit} \times \text{Number of Months} = 150 \times 8 = ₹1200 \]

### Step 2: Calculate the Interest Earned
The interest for a recurring deposit is calculated using the formula for simple interest:
\[ \text{Interest} = \frac{P \times n \times (n + 1)}{24 \times 100} \times r \]
Where:
- \(P\) is the principal amount for one month (₹150),
- \(n\) is the number of months (8),
- \(r\) is the rate of interest (8% per annum).

First, we need to find the effective principal for the total duration:
\[ \text{Effective Principal} = 150 \times 8 = ₹1200 \]
Now, substituting the values into the interest formula:
\[ \text{Interest} = \frac{150 \times 8 \times (8 + 1)}{24} \times \frac{8}{100} \]
Calculating the components:
- \(n + 1 = 8 + 1 = 9\)
- Now substituting:
\[ \text{Interest} = \frac{150 \times 8 \times 9}{24} \times \frac{8}{100} \]
Calculating:
\[ = \frac{10800}{24} \times \frac{8}{100} = 450 \times \frac{8}{100} = 36 \]
So, the total interest earned is ₹36.

### Step 3: Calculate the Maturity Value
The maturity value (M) is the sum of the total principal and the interest earned:
\[ M = \text{Principal Amount} + \text{Interest} = 1200 + 36 = ₹1236 \]

### Final Answer
The maturity value of Amit's deposits after 8 months is ₹1236.

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