The number of trees in a town is `17640`. If the numbers of trees increases annually at the rate of `5%` then how many trees were there 2 years ago ?

Options

A. `14000`
B. `15000`
C. `16000`
D. `19450`

Answer

To find out how many trees were there 2 years ago, we need to work backwards using the given annual increase rate of 5%.

### Step-by-Step Solution:

1. **Identify the Present Value (PV)**:
The current number of trees is given as 17,640.

2. **Determine the Growth Rate**:
The trees increase at a rate of 5% per year. This means that each year, the number of trees is multiplied by 1.05 (which is 100% + 5%).

3. **Calculate the Number of Trees 1 Year Ago**:
To find the number of trees 1 year ago, we can use the formula:
\[ \text{Number of trees 1 year ago} = \frac{\text{Current number of trees}}{1 + \text{Growth Rate}} \]
Substituting the values:
\[ \text{Number of trees 1 year ago} = \frac{17640}{1.05} \approx 16800 \]

4. **Calculate the Number of Trees 2 Years Ago**:
Now, we will use the same formula to find the number of trees 2 years ago:
\[ \text{Number of trees 2 years ago} = \frac{\text{Number of trees 1 year ago}}{1 + \text{Growth Rate}} \]
Substituting the values:
\[ \text{Number of trees 2 years ago} = \frac{16800}{1.05} \approx 16000 \]

5. **Final Answer**:
The number of trees in the town 2 years ago was approximately **16,000**.