Ramesh deposits 2,400 per month in a recurring deposit scheme of a bank for one year. If he gets 1248 as interest at the time of maturity, find the rate of interest Also, find the maturity value of this deposit.

Answer

To solve the problem step by step, we will first find the rate of interest and then calculate the maturity value of the deposit.

### Step 1: Identify the given values
- Monthly deposit (P) = 2400
- Total number of months (n) = 12
- Total interest earned (SI) = 1248

### Step 2: Use the formula for Simple Interest (SI)
The formula for Simple Interest is given by:
\[ SI = \frac{P \times n \times (n + 1)}{2} \times \frac{R}{100} \]
Where:
- \( P \) = monthly deposit
- \( n \) = number of months
- \( R \) = rate of interest

### Step 3: Substitute the known values into the formula
Substituting the values into the formula:
\[ 1248 = \frac{2400 \times 12 \times (12 + 1)}{2} \times \frac{R}{100} \]

### Step 4: Simplify the equation
Calculate \( (12 + 1) = 13 \):
\[ 1248 = \frac{2400 \times 12 \times 13}{2} \times \frac{R}{100} \]
Calculate \( \frac{2400 \times 12 \times 13}{2} \):
\[ = \frac{2400 \times 12 \times 13}{2} = 2400 \times 6 \times 13 = 187200 \]
So we have:
\[ 1248 = 187200 \times \frac{R}{100} \]

### Step 5: Solve for R
Rearranging the equation to find \( R \):
\[ R = \frac{1248 \times 100}{187200} \]
Calculating the right side:
\[ R = \frac{124800}{187200} = \frac{1248}{1872} = \frac{8}{13} \]
Calculating further gives:
\[ R \approx 8\% \]

### Step 6: Calculate the maturity value
The maturity value (MV) is calculated as:
\[ MV = \text{Total Principal} + \text{Interest} \]
Total Principal for one year is:
\[ \text{Total Principal} = P \times n = 2400 \times 12 = 28800 \]
Now, add the interest:
\[ MV = 28800 + 1248 = 30048 \]

### Final Answers
- Rate of Interest (R) = 8%
- Maturity Value (MV) = 30048