The population of a town is 125000. It is increasing at the rate of 2% per annum. What will be its population after 3 years?

Options

A. 142651
B. 132651
C. 232651
D. 332651

Answer

To solve the problem of finding the population of a town after 3 years given an initial population and a rate of increase, we can follow these steps:

### Step 1: Identify the given values
- Present Population (P) = 125,000
- Rate of increase (R) = 2% per annum
- Time (T) = 3 years

### Step 2: Write the formula for compound interest
The formula for calculating the future population using compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
where:
- \(A\) = future population
- \(P\) = present population
- \(R\) = rate of increase
- \(T\) = time in years

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ A = 125000 \left(1 + \frac{2}{100}\right)^3 \]

### Step 4: Simplify the expression inside the parentheses
Calculating the term inside the parentheses:
\[ 1 + \frac{2}{100} = 1 + 0.02 = 1.02 \]

### Step 5: Raise the result to the power of 3
Now, we need to calculate:
\[ A = 125000 \times (1.02)^3 \]

Calculating \( (1.02)^3 \):
\[ (1.02)^3 = 1.061208 \]

### Step 6: Multiply by the present population
Now, we multiply this result by the present population:
\[ A = 125000 \times 1.061208 \]
Calculating this gives:
\[ A \approx 132651 \]

### Step 7: Conclusion
Thus, the population of the town after 3 years will be approximately **132,651**.

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