The population of a city increases at the rate of 15% pa. If its population was 4000 at the end of year 2013 , then what will be its population at the end of year 2015.

Answer

To find the population of the city at the end of 2015, given that it increases at a rate of 15% per annum and was 4000 at the end of 2013, we can use the formula for compound interest:

\[ A = P(1 + r)^n \]

Where:
- \( A \) = the amount of population after \( n \) years
- \( P \) = the initial population (4000)
- \( r \) = the rate of increase (15% or 0.15)
- \( n \) = the number of years (from 2013 to 2015, which is 2 years)

### Step 1: Identify the values
- Initial population \( P = 4000 \)
- Rate of increase \( r = 15\% = 0.15 \)
- Number of years \( n = 2 \)

### Step 2: Substitute the values into the formula
\[ A = 4000(1 + 0.15)^2 \]

### Step 3: Calculate \( (1 + 0.15) \)
\[ 1 + 0.15 = 1.15 \]

### Step 4: Calculate \( (1.15)^2 \)
\[ (1.15)^2 = 1.3225 \]

### Step 5: Substitute back into the formula
\[ A = 4000 \times 1.3225 \]

### Step 6: Calculate \( A \)
\[ A = 5290 \]

### Conclusion
The population of the city at the end of 2015 will be **5290**.

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