Ashok deposits Rs 3,200 per month in a cumulative deposit account for 3 years at the rate of 9% per annum. Find the maturity value of this account.

Answer

To find the maturity value of Ashok's cumulative deposit account, we will follow these steps:

### Step 1: Identify the values
- Monthly deposit (P) = Rs 3,200
- Time period (T) = 3 years = 36 months (3 years × 12 months/year)
- Rate of interest (R) = 9% per annum

### Step 2: Calculate the total number of deposits
The total number of deposits made is 36 months.

### Step 3: Calculate the interest earned
The formula for calculating the interest (I) on a cumulative deposit account is given by:
\[ I = P \times \frac{N(N + 1)}{2} \times \frac{R}{100 \times 12} \]
Where:
- \( N \) = total number of months (36)
- \( P \) = monthly deposit (3200)
- \( R \) = annual interest rate (9%)

Substituting the values into the formula:
\[ I = 3200 \times \frac{36 \times (36 + 1)}{2} \times \frac{9}{100 \times 12} \]

Calculating \( N(N + 1) \):
\[ N(N + 1) = 36 \times 37 = 1332 \]
Now substituting this back into the interest formula:
\[ I = 3200 \times \frac{1332}{2} \times \frac{9}{1200} \]
Calculating \( \frac{1332}{2} = 666 \):
\[ I = 3200 \times 666 \times \frac{9}{1200} \]
Calculating \( \frac{9}{1200} = 0.0075 \):
\[ I = 3200 \times 666 \times 0.0075 \]
Calculating \( 3200 \times 666 = 2131200 \):
\[ I = 2131200 \times 0.0075 = 15984 \]

### Step 4: Calculate the total amount deposited
The total amount deposited over 36 months is:
\[ \text{Total Deposit} = P \times N = 3200 \times 36 = 115200 \]

### Step 5: Calculate the maturity value
The maturity value (MV) is the total amount deposited plus the interest earned:
\[ MV = \text{Total Deposit} + I = 115200 + 15984 = 131184 \]

### Final Answer
The maturity value of Ashok's account after 3 years is Rs 131,184.

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