Mr. Britto deposits a certain sum of money each month in a Recurring Deposit Account of a bank. If the rate of interest is of 8% per annum and Mr. Britto gets Rs 8,088 from the bank after 3 years, find the value of his monthly instalment.

Answer

To find Mr. Britto's monthly installment in his Recurring Deposit Account, we can follow these steps:

### Step 1: Identify the given data
- Maturity Value (M) = Rs 8,088
- Time period (n) = 3 years = 3 × 12 = 36 months
- Rate of Interest (r) = 8% per annum

### Step 2: Define the monthly installment
Let the monthly installment be denoted as \( p \).

### Step 3: Calculate the total deposit
The total deposit made by Mr. Britto over the 36 months is:
\[ \text{Total Deposit} = p \times n = p \times 36 = 36p \]

### Step 4: Calculate the interest received
The interest received can be calculated as:
\[ \text{Interest} = \text{Maturity Value} - \text{Total Deposit} = 8088 - 36p \]

### Step 5: Use the formula for Simple Interest
The formula for Simple Interest (SI) in a Recurring Deposit Account is:
\[ SI = \frac{p \times n \times (n + 1)}{2 \times 12} \times \frac{r}{100} \]
Substituting the known values:
- \( n = 36 \)
- \( r = 8 \)

So, we have:
\[ SI = \frac{p \times 36 \times 37}{2 \times 12} \times \frac{8}{100} \]

### Step 6: Simplify the SI formula
Calculating the constants:
\[ SI = \frac{p \times 36 \times 37}{24} \times \frac{8}{100} \]
\[ = \frac{p \times 36 \times 37 \times 8}{2400} \]

### Step 7: Set up the equation
Now, we equate the interest received to the calculated SI:
\[ 8088 - 36p = \frac{p \times 36 \times 37 \times 8}{2400} \]

### Step 8: Solve for \( p \)
Rearranging gives us:
\[ 8088 = 36p + \frac{p \times 36 \times 37 \times 8}{2400} \]

To simplify, we can multiply through by 2400 to eliminate the fraction:
\[ 8088 \times 2400 = 36p \times 2400 + p \times 36 \times 37 \times 8 \]

Calculating \( 8088 \times 2400 \):
\[ = 19411200 \]

Now, simplifying the right side:
\[ = 86400p + 1776p \]
\[ = (86400 + 1776)p = 88176p \]

Now we have:
\[ 19411200 = 88176p \]

### Step 9: Isolate \( p \)
Dividing both sides by 88176 gives:
\[ p = \frac{19411200}{88176} \]

Calculating \( p \):
\[ p = 220 \]

### Conclusion
Thus, Mr. Britto's monthly installment is Rs 220.

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