The population of a village is 5000 and it increases at the rate of 2% every year. After 2 years, the population will be :

Options

A. 5116
B. 5202
C. 5200
D. 5204

Answer

To solve the problem of calculating the population of a village after 2 years with an initial population of 5000 and an annual increase of 2%, we can follow these steps:

### Step 1: Understand the Initial Population
The initial population of the village is given as 5000.

### Step 2: Calculate the Population After the First Year
To find the population after the first year, we need to calculate the increase due to the 2% growth.

- **Increase in Population After 1 Year**:
\[ \text{Increase} = \text{Initial Population} \times \text{Growth Rate} \]
\[ \text{Increase} = 5000 \times \frac{2}{100} = 5000 \times 0.02 = 100 \]

- **Population After 1 Year**:
\[ \text{Population After 1 Year} = \text{Initial Population} + \text{Increase} \]
\[ \text{Population After 1 Year} = 5000 + 100 = 5100 \]

### Step 3: Calculate the Population After the Second Year
Now, we need to calculate the population after the second year using the new population from the end of the first year (5100).

- **Increase in Population After 2 Years**:
\[ \text{Increase} = \text{Population After 1 Year} \times \text{Growth Rate} \]
\[ \text{Increase} = 5100 \times \frac{2}{100} = 5100 \times 0.02 = 102 \]

- **Population After 2 Years**:
\[ \text{Population After 2 Years} = \text{Population After 1 Year} + \text{Increase} \]
\[ \text{Population After 2 Years} = 5100 + 102 = 5202 \]

### Final Answer
The population of the village after 2 years will be **5202**.

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