To solve the problem step by step, we will follow the information provided in the question and the video transcript.
### Step 1: Identify the Given Data
- Maturity Value (M) = ₹ 11,364
- Monthly Deposit (P) = ₹ 200
- Time Period (in years) = 4 years
### Step 2: Convert Time Period to Months
Since the deposits are made monthly, we need to convert the time period from years to months.
- Time Period (n) = 4 years × 12 months/year = 48 months
### Step 3: Calculate Total Deposit
The total deposit (TD) can be calculated using the formula:
\[ \text{Total Deposit} = \text{Monthly Deposit} \times \text{Time Period} \]
\[ \text{TD} = P \times n = 200 \times 48 = ₹ 9,600 \]
### Step 4: Calculate Simple Interest
The simple interest (SI) can be calculated as the difference between the maturity value and the total deposit.
\[ \text{SI} = M - \text{TD} \]
\[ \text{SI} = 11,364 - 9,600 = ₹ 1,764 \]
### Step 5: Use the Formula for Simple Interest in Recurring Deposits
The formula for calculating simple interest in a recurring deposit account is:
\[ \text{SI} = \frac{P \times n \times (n + 1) \times r}{2400} \]
Where:
- P = Monthly Deposit
- n = Time Period (in months)
- r = Rate of Interest (in %)
### Step 6: Substitute the Values into the Formula
Now, we can substitute the known values into the formula to find the rate of interest (r):
\[ 1,764 = \frac{200 \times 48 \times (48 + 1) \times r}{2400} \]
\[ 1,764 = \frac{200 \times 48 \times 49 \times r}{2400} \]
### Step 7: Simplify the Equation
First, calculate \( 200 \times 48 \times 49 \):
- \( 200 \times 48 = 9,600 \)
- \( 9,600 \times 49 = 470,400 \)
Now, substitute this back into the equation:
\[ 1,764 = \frac{470,400 \times r}{2400} \]
### Step 8: Solve for r
Multiply both sides by 2400 to eliminate the fraction:
\[ 1,764 \times 2400 = 470,400 \times r \]
\[ 4,233,600 = 470,400 \times r \]
Now, divide both sides by 470,400 to solve for r:
\[ r = \frac{4,233,600}{470,400} \]
\[ r = 9 \]
### Step 9: Conclusion
The rate of interest (r) is:
\[ \text{Rate of Interest} = 9\% \]
