Puneet Has a Recurring Deposit Account in the Bank of Baroda and Deposits Rs 140 per Month for 4 Years. If He Gets Rs 8,092 on Maturity, Find the Rate of Interest Given by the Bank.

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the given values
- Monthly deposit (P) = Rs 140
- Total duration = 4 years
- Total maturity amount (A) = Rs 8092

### Step 2: Calculate the total number of months
Total months (N) = 4 years × 12 months/year = 48 months

### Step 3: Use the formula for Simple Interest (SI) for Recurring Deposits
The formula for calculating the Simple Interest (SI) for a recurring deposit is:
\[ SI = \frac{P \times N \times (N + 1)}{2 \times 12} \times \frac{R}{100} \]
Where:
- P = monthly deposit
- N = total number of months
- R = rate of interest per annum

### Step 4: Substitute the known values into the formula
Substituting the values we have:
\[ SI = \frac{140 \times 48 \times (48 + 1)}{2 \times 12} \times \frac{R}{100} \]
Calculating \(N + 1\):
\[ N + 1 = 48 + 1 = 49 \]
Now substituting this back:
\[ SI = \frac{140 \times 48 \times 49}{2 \times 12} \times \frac{R}{100} \]

### Step 5: Simplify the expression
Calculating the numerator:
\[ 140 \times 48 \times 49 = 140 \times 2352 = 329280 \]
Now substituting this back into the formula:
\[ SI = \frac{329280}{24} \times \frac{R}{100} \]
Calculating \( \frac{329280}{24} \):
\[ \frac{329280}{24} = 13720 \]
So,
\[ SI = 13720 \times \frac{R}{100} \]
This simplifies to:
\[ SI = 137.20R \]

### Step 6: Calculate the total principal amount (P)
The total principal amount (P) over 48 months is:
\[ P = 140 \times 48 = 6720 \]

### Step 7: Set up the equation for maturity amount
The maturity amount (A) is given by:
\[ A = P + SI \]
Substituting the values we have:
\[ 8092 = 6720 + 137.20R \]

### Step 8: Solve for R
Rearranging the equation:
\[ 8092 - 6720 = 137.20R \]
Calculating the left side:
\[ 1372 = 137.20R \]
Now, divide both sides by 137.20:
\[ R = \frac{1372}{137.20} \]
Calculating this gives:
\[ R = 10 \]

### Step 9: Conclusion
The rate of interest (R) is:
\[ \text{Rate of Interest} = 10\% \text{ per annum} \]

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