Mr. R.K. Nair gets `₹ 6,455` at the end of one year at the rate of `14%` per annum in a Recurring Deposit Account. Find the monthly instalment.

Answer

To solve the problem of finding the monthly installment for Mr. R.K. Nair's Recurring Deposit Account, we can follow these steps:

### Step 1: Identify the given data
- Maturity Value (MV) = ₹6,455
- Rate of Interest (r) = 14% per annum
- Time period (n) = 1 year = 12 months

### Step 2: Define the monthly installment
Let the monthly installment be represented as \( x \).

### Step 3: Calculate the Total Deposit
The total deposit (TD) over the period of one year can be calculated as:
\[ TD = \text{Monthly Installment} \times \text{Number of Months} = x \times 12 = 12x \]

### Step 4: Calculate the Simple Interest (SI)
The formula for calculating Simple Interest in a Recurring Deposit Account is:
\[ SI = \frac{P \times n \times (n + 1)}{2 \times 12} \times \frac{r}{100} \]
Where:
- \( P \) = Monthly installment = \( x \)
- \( n \) = Number of months = 12
- \( r \) = Rate of interest = 14%

Substituting the values:
\[ SI = \frac{x \times 12 \times (12 + 1)}{2 \times 12} \times \frac{14}{100} \]
\[ SI = \frac{x \times 12 \times 13}{2 \times 12} \times \frac{14}{100} \]
\[ SI = \frac{x \times 13}{2} \times \frac{14}{100} \]
\[ SI = \frac{91x}{100} \]

### Step 5: Write the equation for Maturity Value
The Maturity Value (MV) is the sum of the Total Deposit and the Simple Interest:
\[ MV = TD + SI \]
Substituting the expressions we found:
\[ 6455 = 12x + \frac{91x}{100} \]

### Step 6: Solve for \( x \)
To solve for \( x \), first, we need a common denominator:
\[ 6455 = \frac{1200x}{100} + \frac{91x}{100} \]
\[ 6455 = \frac{1200x + 91x}{100} \]
\[ 6455 = \frac{1291x}{100} \]
Now, multiply both sides by 100:
\[ 645500 = 1291x \]
Now, divide both sides by 1291:
\[ x = \frac{645500}{1291} \approx 500 \]

### Conclusion
Thus, the monthly installment \( x \) is ₹500.