The population of a town increases at the rate of 15% per annum. If the present population is 108445 of town, then what was the population 2 years ago?

Options

A. 72000
B. 79000
C. 82000
D. 85000

Answer

To find the population of the town two years ago, given that the current population is 108,445 and it increases at a rate of 15% per annum, we can use the formula for population growth.

1. **Understanding the Growth Rate**:
The population increases by 15% each year. This means that if the population two years ago was \( P \), then after one year it would be \( P \times (1 + 0.15) = P \times 1.15 \). After the second year, it would be \( P \times 1.15 \times 1.15 = P \times (1.15)^2 \).

2. **Setting Up the Equation**:
We know the current population is 108,445. Therefore, we can set up the equation:
\[ P \times (1.15)^2 = 108445 \]

3. **Calculating \( (1.15)^2 \)**:
First, we need to calculate \( (1.15)^2 \):
\[ (1.15)^2 = 1.3225 \]

4. **Rearranging the Equation**:
Now we can rearrange the equation to find \( P \):
\[ P = \frac{108445}{1.3225} \]

5. **Performing the Division**:
Now we will perform the division:
\[ P \approx \frac{108445}{1.3225} \approx 81900 \]

6. **Final Calculation**:
After calculating, we find:
\[ P \approx 81900 \]

Thus, the population of the town two years ago was approximately **82,000**.