The population of a city at present is 80000. If it increase by 5% per year, what will be the population after 3 years?

Options

A. 88200
B. 84000
C. 92610
D. 86610

Answer

To find the population of a city after 3 years with an annual increase of 5%, we can use the formula for compound interest, which is also applicable for population growth:

\[ P = P_0 \times (1 + r)^n \]

Where:
- \( P \) is the future population.
- \( P_0 \) is the current population.
- \( r \) is the rate of increase (as a decimal).
- \( n \) is the number of years.

### Step-by-Step Solution:

1. **Identify the current population (P0)**:
- The current population \( P_0 \) is 80,000.

2. **Identify the rate of increase (r)**:
- The rate of increase is 5%, which can be expressed as a decimal:
\[ r = \frac{5}{100} = 0.05 \]

3. **Identify the number of years (n)**:
- The number of years \( n \) is 3.

4. **Substitute the values into the formula**:
\[ P = 80000 \times (1 + 0.05)^3 \]

5. **Calculate \( (1 + 0.05) \)**:
\[ 1 + 0.05 = 1.05 \]

6. **Raise \( 1.05 \) to the power of 3**:
\[ (1.05)^3 = 1.157625 \]

7. **Multiply by the current population**:
\[ P = 80000 \times 1.157625 \]
\[ P \approx 92610 \]

8. **Final Result**:
- The population after 3 years will be approximately 92,610.