The population of a town in China increases by 20% every year If its present population is 2,16,000 , find its population after 2 years

Answer

To find the population of a town in China after 2 years given that it increases by 20% every year, we can use the compound interest formula. Here’s the step-by-step solution:

### Step 1: Identify the given values
- Present population (P) = 216,000
- Rate of increase (r) = 20%
- Time (t) = 2 years

### Step 2: Write the compound interest formula
The formula for compound interest is:
\[ A = P \times \left(1 + \frac{r}{100}\right)^t \]
Where:
- \( A \) = Amount after time \( t \)
- \( P \) = Principal amount (initial population)
- \( r \) = Rate of interest (percentage increase)
- \( t \) = Time in years

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ A = 216,000 \times \left(1 + \frac{20}{100}\right)^2 \]

### Step 4: Simplify the expression
Calculate \( 1 + \frac{20}{100} \):
\[ 1 + \frac{20}{100} = 1 + 0.2 = 1.2 \]
Now substitute this back into the equation:
\[ A = 216,000 \times (1.2)^2 \]

### Step 5: Calculate \( (1.2)^2 \)
\[ (1.2)^2 = 1.44 \]
Now substitute this value back:
\[ A = 216,000 \times 1.44 \]

### Step 6: Perform the multiplication
Now calculate:
\[ A = 216,000 \times 1.44 = 311,040 \]

### Step 7: Conclusion
The population of the town after 2 years will be **311,040**.

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