Sonia had recurring deposite account in a bank and deposited Rs 600 per month for `2(1)/(2)` years. If the rate of interest was 10% p.a., find the maturity value of this account.

Answer

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

### Step 1: Understand the Variables
- **P** = Amount deposited per month = Rs 600
- **n** = Total number of months the deposits were made = 2.5 years = 2.5 × 12 = 30 months
- **r** = Rate of interest per annum = 10%

### Step 2: Use the Maturity Value Formula
The formula for the maturity value (MV) of a recurring deposit is given by:

\[ MV = P \times n + \frac{P \times n \times (n + 1)}{2 \times 12} \times \frac{r}{100} \]

### Step 3: Substitute the Values into the Formula
Now, we will substitute the values of P, n, and r into the formula:

\[ MV = 600 \times 30 + \frac{600 \times 30 \times (30 + 1)}{2 \times 12} \times \frac{10}{100} \]

### Step 4: Calculate Each Component
1. Calculate the total amount deposited:
\[ 600 \times 30 = 18000 \]

2. Calculate the interest earned:
- First, calculate \( n + 1 \):
\[ 30 + 1 = 31 \]
- Now, calculate the interest component:
\[ \frac{600 \times 30 \times 31}{2 \times 12} \times \frac{10}{100} \]
- Calculate \( \frac{600 \times 30 \times 31}{2 \times 12} \):
\[ = \frac{600 \times 30 \times 31}{24} = \frac{558000}{24} = 23250 \]
- Now, calculate the interest:
\[ 23250 \times \frac{10}{100} = 2325 \]

### Step 5: Add the Total Deposits and Interest
Now, we can find the maturity value by adding the total deposits and the interest earned:

\[ MV = 18000 + 2325 = 20325 \]

### Final Answer
The maturity value of Sonia's recurring deposit account is **Rs 20325**.

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