Govinda opened a R.D. acount in a bank for 2 years 4 months. If the rate of interest is 8% per year and the bank pays him Rs 7,369.60 on maturity, find how much per month did Govinda deposit ?

Answer

To find out how much Govinda deposited per month in his R.D. account, we can follow these steps:

### Step 1: Convert the time period into months
Govinda opened the account for 2 years and 4 months.
- Convert years into months:
\[ 2 \text{ years} = 2 \times 12 = 24 \text{ months} \]
- Add the additional 4 months:
\[ \text{Total time} = 24 + 4 = 28 \text{ months} \]

**Hint:** Remember that 1 year equals 12 months.

### Step 2: Define the variables
Let \( P \) be the amount deposited per month. The total number of months is \( n = 28 \).

### Step 3: Use the formula for maturity value
The maturity value \( M \) is given by:
\[ M = P \times n + \text{Interest} \]
Where the interest can be calculated using the formula:
\[ \text{Interest} = \frac{P \times n \times (n + 1)}{2 \times 12} \times \frac{r}{100} \]
Given \( r = 8\% \).

### Step 4: Substitute the known values
Substituting \( M = 7369.60 \), \( n = 28 \), and \( r = 8\):
\[ 7369.60 = P \times 28 + \frac{P \times 28 \times 29}{2 \times 12} \times \frac{8}{100} \]

### Step 5: Simplify the interest term
Calculating the interest term:
\[ \text{Interest} = \frac{P \times 28 \times 29}{24} \times \frac{8}{100} \]
This simplifies to:
\[ \text{Interest} = \frac{P \times 28 \times 29 \times 8}{2400} \]

### Step 6: Combine the equations
Now substitute the interest back into the maturity value equation:
\[ 7369.60 = P \times 28 + \frac{P \times 28 \times 29 \times 8}{2400} \]

### Step 7: Solve for \( P \)
Factor out \( P \):
\[ 7369.60 = P \left(28 + \frac{28 \times 29 \times 8}{2400}\right) \]
Calculating the term inside the parentheses:
\[ \frac{28 \times 29 \times 8}{2400} = \frac{6512}{2400} = 2.7133 \]
So,
\[ 7369.60 = P (28 + 2.7133) \]
\[ 7369.60 = P \times 30.7133 \]
Now, isolate \( P \):
\[ P = \frac{7369.60}{30.7133} \]
Calculating \( P \):
\[ P \approx 240 \]

### Final Answer
Thus, the amount that Govinda deposited per month is **Rs 240**.

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