P deposite Rs. 5000 in NSC at 2% per annum and Rs. 2000 in mutual funds at 4% per annum. Find the rate of interest for the whole sum.

Answer

To find the rate of interest for the whole sum deposited by P, we will follow these steps:

### Step 1: Identify the amounts and rates of interest
- Amount deposited in NSC = Rs. 5000 at 2% per annum
- Amount deposited in mutual funds = Rs. 2000 at 4% per annum

### Step 2: Calculate the simple interest for each investment
The formula for simple interest (SI) is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where \( P \) is the principal amount, \( R \) is the rate of interest, and \( T \) is the time in years.

**For NSC:**
- Principal (P) = Rs. 5000
- Rate (R) = 2%
- Time (T) = 1 year

Calculating SI for NSC:
\[ \text{SI}_{\text{NSC}} = \frac{5000 \times 2 \times 1}{100} = \frac{10000}{100} = Rs. 100 \]

**For Mutual Funds:**
- Principal (P) = Rs. 2000
- Rate (R) = 4%
- Time (T) = 1 year

Calculating SI for Mutual Funds:
\[ \text{SI}_{\text{Mutual Funds}} = \frac{2000 \times 4 \times 1}{100} = \frac{8000}{100} = Rs. 80 \]

### Step 3: Calculate the total simple interest
Now, we add the simple interests from both investments:
\[ \text{Total SI} = \text{SI}_{\text{NSC}} + \text{SI}_{\text{Mutual Funds}} \]
\[ \text{Total SI} = 100 + 80 = Rs. 180 \]

### Step 4: Calculate the total principal amount
Now, we find the total principal amount invested:
\[ \text{Total Principal} = 5000 + 2000 = Rs. 7000 \]

### Step 5: Calculate the overall rate of interest
The overall rate of interest can be calculated using the formula:
\[ \text{Rate} = \left( \frac{\text{Total SI}}{\text{Total Principal}} \times 100 \right) \]

Substituting the values:
\[ \text{Rate} = \left( \frac{180}{7000} \times 100 \right) \]
\[ \text{Rate} = \left( \frac{18000}{7000} \right) \]
\[ \text{Rate} = 2.57\% \]

### Final Answer:
The rate of interest for the whole sum is approximately **2.57% per annum**.

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