If the population P of a town increases at R% per annum, then its population after 5 years is …….

Answer

To find the population of a town after 5 years given that it increases at R% per annum, we can use the formula for compound interest, which is also applicable for population growth. The formula is:

\[ A = P \left(1 + \frac{R}{100}\right)^n \]

Where:
- \( A \) is the amount (or population after n years),
- \( P \) is the principal amount (initial population),
- \( R \) is the rate of increase (in percentage),
- \( n \) is the number of years.

### Step-by-Step Solution:

1. **Identify the Variables**:
- Initial population \( P \) (the current population of the town).
- Rate of increase \( R \) (the percentage increase in population per annum).
- Time period \( n \) (which is given as 5 years).

2. **Substitute the Values into the Formula**:
- We know \( n = 5 \) years.
- Substitute \( n \) into the formula:
\[ A = P \left(1 + \frac{R}{100}\right)^5 \]

3. **Calculate the Population After 5 Years**:
- The expression \( \left(1 + \frac{R}{100}\right)^5 \) represents the growth factor over 5 years.
- Therefore, the population after 5 years can be expressed as:
\[ A = P \left(1 + \frac{R}{100}\right)^5 \]

4. **Final Expression**:
- The final expression for the population after 5 years is:
\[ A = P \left(1 + \frac{R}{100}\right)^5 \]

### Final Answer:
The population after 5 years is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^5 \]