Reena deposited `₹18,000` in a bank. She withdrew `₹5000` after `4` years. At the end of `9` years, she receives an amount of `₹21,220`. Find the rate of interest.

Answer

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

### Step 1: Understand the Problem
Reena deposited ₹18,000 in a bank. After 4 years, she withdrew ₹5,000. At the end of 9 years, she received a total amount of ₹21,220. We need to find the rate of interest.

### Step 2: Calculate the Principal After Withdrawal
After 4 years, Reena withdrew ₹5,000. Therefore, the principal amount remaining after 4 years is:
\[ \text{Remaining Principal} = 18,000 - 5,000 = 13,000 \]

### Step 3: Calculate the Total Amount Received
At the end of 9 years, Reena received ₹21,220. This amount includes the principal and the simple interest earned.

### Step 4: Calculate the Total Simple Interest Earned
The total simple interest (SI) earned can be calculated as:
\[ \text{Total Amount} = \text{Principal} + \text{Simple Interest} \]
Thus,
\[ \text{Simple Interest} = \text{Total Amount} - \text{Principal} \]
Substituting the values:
\[ \text{Simple Interest} = 21,220 - 13,000 = 8,220 \]

### Step 5: Calculate Simple Interest for the First 4 Years
Using the formula for simple interest:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
For the first 4 years:
\[ \text{SI}_1 = \frac{18,000 \times R \times 4}{100} \]
This can be simplified to:
\[ \text{SI}_1 = 720R \quad \text{(Equation 1)} \]

### Step 6: Calculate Simple Interest for the Next 5 Years
After 4 years, the principal is ₹13,000. For the next 5 years:
\[ \text{SI}_2 = \frac{13,000 \times R \times 5}{100} \]
This can be simplified to:
\[ \text{SI}_2 = 650R \quad \text{(Equation 2)} \]

### Step 7: Set Up the Equation
The total simple interest earned over 9 years is the sum of the two simple interests:
\[ \text{SI}_1 + \text{SI}_2 = 8,220 \]
Substituting the values from Equation 1 and Equation 2:
\[ 720R + 650R = 8,220 \]
Combining like terms:
\[ 1370R = 8,220 \]

### Step 8: Solve for R
To find R, divide both sides by 1370:
\[ R = \frac{8,220}{1,370} \]
Calculating this gives:
\[ R = 6 \]

### Final Answer
The rate of interest is **6%**.

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