The present population of a city is 180000. If it increases at the rate of 10% per annum, its population after 2 years will be :

Options

A. 207800
B. 227800
C. 217800
D. 237800

Answer

To find the population of a city after 2 years given its current population and annual growth rate, we can use the formula for compound interest, which is applicable here since the population increases at a constant percentage rate each year.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Present Population (P) = 180,000
- Rate of Increase (r) = 10% per annum
- Time (t) = 2 years

2. **Convert the Percentage Rate to Decimal:**
- The rate of increase in decimal form is:
\[ r = \frac{10}{100} = 0.10 \]

3. **Use the Compound Interest Formula:**
- The formula to calculate the future population after t years is:
\[ \text{Future Population} = P \times (1 + r)^t \]
- Substituting the values we have:
\[ \text{Future Population} = 180,000 \times (1 + 0.10)^2 \]

4. **Calculate \( (1 + r)^t \):**
- First, calculate \( (1 + 0.10) = 1.10 \).
- Now, calculate \( (1.10)^2 \):
\[ (1.10)^2 = 1.10 \times 1.10 = 1.21 \]

5. **Calculate the Future Population:**
- Now substitute back into the formula:
\[ \text{Future Population} = 180,000 \times 1.21 \]
- Perform the multiplication:
\[ \text{Future Population} = 217,800 \]

6. **Conclusion:**
- The population of the city after 2 years will be **217,800**.