Mr. Sonu has a recurring deposit account and deposits Rs. 750 per month for 2 years. If he gets Rs. 19125 at the time of maturity, find the rate of interest.

Answer

To find the rate of interest for Mr. Sonu's recurring deposit account, we will follow these steps:

### Step 1: Identify the given values
- Monthly deposit (P) = Rs. 750
- Time period (T) = 2 years = 24 months
- Total amount received at maturity (MV) = Rs. 19125

### Step 2: Use the formula for maturity value of a recurring deposit
The formula for the maturity value (MV) of a recurring deposit is given by:
\[ MV = P \times T + \frac{P \times T \times (T + 1)}{2400} \times R \]
Where:
- \(P\) = monthly deposit
- \(T\) = total number of months
- \(R\) = rate of interest (in percentage)

### Step 3: Substitute the known values into the formula
Substituting the values we have:
\[ 19125 = 750 \times 24 + \frac{750 \times 24 \times (24 + 1)}{2400} \times R \]

### Step 4: Calculate the first part of the equation
Calculate \(750 \times 24\):
\[ 750 \times 24 = 18000 \]
So the equation becomes:
\[ 19125 = 18000 + \frac{750 \times 24 \times 25}{2400} \times R \]

### Step 5: Simplify the equation
Now calculate \(750 \times 24 \times 25\):
\[ 750 \times 24 \times 25 = 450000 \]
Now substitute this back into the equation:
\[ 19125 = 18000 + \frac{450000}{2400} \times R \]

### Step 6: Calculate \(\frac{450000}{2400}\)
\[ \frac{450000}{2400} = 187.5 \]
So the equation simplifies to:
\[ 19125 = 18000 + 187.5R \]

### Step 7: Rearrange the equation to solve for \(R\)
Subtract 18000 from both sides:
\[ 19125 - 18000 = 187.5R \]
\[ 1125 = 187.5R \]

### Step 8: Solve for \(R\)
Now divide both sides by 187.5:
\[ R = \frac{1125}{187.5} = 6 \]

### Step 9: Conclusion
Thus, the rate of interest \(R\) is 6%.