Population of a town increases by 12% every year. If the popula tion of town will be 188160 after 2 years, then what is its present population?

Options

A. 150000
B. 160000
C. 155000
D. 165000

Answer

To find the present population of the town given that it increases by 12% every year and will be 188,160 after 2 years, we can use the formula for compound interest:

**Step 1: Understand the formula**
The formula for calculating the future amount (A) based on the present value (P), rate (r), and time (t) is:
\[ A = P \times (1 + \frac{r}{100})^t \]

**Step 2: Identify the values**
From the question:
- Future Amount (A) = 188,160
- Rate (r) = 12%
- Time (t) = 2 years

**Step 3: Substitute the values into the formula**
We need to find the present population (P). Rearranging the formula gives us:
\[ P = \frac{A}{(1 + \frac{r}{100})^t} \]

Substituting the known values:
\[ P = \frac{188160}{(1 + \frac{12}{100})^2} \]

**Step 4: Simplify the expression**
Calculating \( (1 + \frac{12}{100}) \):
\[ 1 + \frac{12}{100} = 1 + 0.12 = 1.12 \]

Now, we need to calculate \( (1.12)^2 \):
\[ (1.12)^2 = 1.2544 \]

**Step 5: Calculate the present population**
Now substitute back into the equation for P:
\[ P = \frac{188160}{1.2544} \]

Calculating this gives:
\[ P \approx 150000 \]

Thus, the present population of the town is approximately **150,000**.