Mohan deposited `₹ 80` per month in a cumulative (recurring) deposit account for six years. Find the amount payable to him on maturity, if the rate of interest is `6%` per annum.

Answer

To find the amount payable to Mohan on maturity after depositing ₹80 per month for six years in a recurring deposit account at an interest rate of 6% per annum, we can follow these steps:

### Step 1: Gather the Given Information
- Monthly deposit (P) = ₹80
- Duration (T) = 6 years
- Rate of interest (R) = 6% per annum

### Step 2: Convert Duration into Months
Since the deposits are made monthly, we need to convert the duration from years to months:
\[ T = 6 \text{ years} \times 12 \text{ months/year} = 72 \text{ months} \]

### Step 3: Calculate the Total Principal Amount
The total principal amount (P_total) is calculated by multiplying the monthly deposit by the total number of months:
\[ P_{\text{total}} = \text{Monthly Deposit} \times \text{Number of Months} \]
\[ P_{\text{total}} = 80 \times 72 = ₹5760 \]

### Step 4: Calculate the Interest Earned
The formula for calculating the interest on a recurring deposit is:
\[ \text{Interest} = \frac{P \times N \times (N + 1)}{24 \times 100} \times R \]
Where:
- P = Monthly deposit
- N = Number of months
- R = Rate of interest

Substituting the values:
\[ \text{Interest} = \frac{80 \times 72 \times (72 + 1)}{24 \times 100} \]
\[ = \frac{80 \times 72 \times 73}{2400} \]

Calculating the values:
1. Calculate \( 72 \times 73 = 5256 \)
2. Then, \( 80 \times 5256 = 420480 \)
3. Finally, divide by 2400:
\[ \text{Interest} = \frac{420480}{2400} = ₹175.2 \]

### Step 5: Calculate the Total Maturity Amount
The total maturity amount (M) is the sum of the total principal and the interest earned:
\[ M = P_{\text{total}} + \text{Interest} \]
\[ M = 5760 + 175.2 = ₹5935.2 \]

### Final Answer
The amount payable to Mohan on maturity is **₹5935.2**.

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