Mohan has a recurring deposit account in a bank for `2` years at `6%` p.a. simple interest. If he gets `₹ 1,200` as interest at the time of maturity find :
(i) the monthly instalment
(ii) the amount of maturity.

Answer

To solve the problem step by step, we will break it down into two parts: finding the monthly installment and then calculating the maturity amount.

### Step 1: Understanding the given information
- Duration of the recurring deposit = 2 years = 24 months
- Rate of interest = 6% per annum
- Total interest earned = ₹1,200

### Step 2: Formula for Simple Interest
The formula for calculating the simple interest for a recurring deposit is:
\[ \text{Simple Interest} = \frac{P \times n \times (n + 1)}{24 \times 100} \]
Where:
- \( P \) = monthly installment
- \( n \) = number of months

### Step 3: Substitute the known values into the formula
We know the total interest earned is ₹1,200, and \( n = 24 \) months. Therefore, we can set up the equation:
\[ 1200 = \frac{P \times 24 \times (24 + 1)}{24 \times 100} \]
This simplifies to:
\[ 1200 = \frac{P \times 24 \times 25}{2400} \]

### Step 4: Simplify the equation
Now, we can simplify the equation:
\[ 1200 = \frac{P \times 600}{2400} \]
\[ 1200 = \frac{P}{4} \]

### Step 5: Solve for \( P \)
To find \( P \), multiply both sides by 4:
\[ P = 1200 \times 4 = 4800 \]

### Step 6: Calculate the monthly installment
Since \( P \) represents the total amount deposited over 24 months, the monthly installment is:
\[ \text{Monthly Installment} = \frac{4800}{24} = 800 \]

### Step 7: Calculate the maturity amount
The maturity amount is the total principal plus the interest earned. The total principal is:
\[ \text{Total Principal} = P \times n = 800 \times 24 = 19200 \]
Now, add the interest earned:
\[ \text{Maturity Amount} = \text{Total Principal} + \text{Interest} = 19200 + 1200 = 20400 \]

### Final Answers
(i) The monthly installment is ₹800.
(ii) The amount of maturity is ₹20,400.

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