Manju invested `₹9000` in a bank. She deposited an additional `₹3000` after `2` years. At the end of `3` years, she received `₹13,200`. Find the rate of interest.

Answer

To find the rate of interest for Manju's investment, we will follow these steps:

### Step 1: Identify the Initial Investment and Additional Deposit
Manju initially invested ₹9000 and deposited an additional ₹3000 after 2 years.

### Step 2: Calculate the Total Amount Received
At the end of 3 years, Manju received ₹13200.

### Step 3: Determine the Simple Interest Earned
The total amount received can be expressed as:
\[ \text{Total Amount} = \text{Principal} + \text{Simple Interest} \]
Here, the principal after 2 years becomes ₹12000 (₹9000 + ₹3000). Therefore, we can express the simple interest earned over the 3 years as:
\[ \text{Simple Interest} = \text{Total Amount} - \text{Principal} \]
\[ \text{Simple Interest} = ₹13200 - ₹12000 = ₹1200 \]

### Step 4: Calculate Simple Interest for Each Period
1. **For the first 2 years** (initial principal of ₹9000):
\[ \text{Simple Interest}_1 = \frac{9000 \times r \times 2}{100} \]

2. **For the last 1 year** (new principal of ₹12000):
\[ \text{Simple Interest}_2 = \frac{12000 \times r \times 1}{100} \]

### Step 5: Combine the Simple Interests
The total simple interest over the 3 years is:
\[ \text{Simple Interest}_1 + \text{Simple Interest}_2 = ₹1200 \]
Substituting the expressions we derived:
\[ \frac{9000 \times r \times 2}{100} + \frac{12000 \times r \times 1}{100} = 1200 \]

### Step 6: Simplify the Equation
Multiplying through by 100 to eliminate the denominator:
\[ 9000 \times r \times 2 + 12000 \times r = 120000 \]
This simplifies to:
\[ 18000r + 12000r = 120000 \]
\[ 30000r = 120000 \]

### Step 7: Solve for the Rate of Interest
Now, divide both sides by 30000 to find \( r \):
\[ r = \frac{120000}{30000} = 4 \]

### Final Answer
The rate of interest is **4%**.

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