1. **State the problem:** A population increases by 5% each year. We need to find the total percentage increase after two years. 2. **Formula used:** When a quantity increases by a percentage $r$ each year, the amount after $n$ years is given by: $$ P_{final} = P_{initial} \times (1 + \frac{r}{100})^n $$ 3. **Apply the formula:** Here, $r = 5$ and $n = 2$. $$ P_{final} = P_{initial} \times (1 + \frac{5}{100})^2 = P_{initial} \times (1.05)^2 $$ 4. **Calculate:** $$ (1.05)^2 = 1.05 \times 1.05 = 1.1025 $$ 5. **Interpretation:** The population after two years is $1.1025$ times the initial population. 6. **Find percentage increase:** $$ \text{Percentage increase} = (1.1025 - 1) \times 100 = 0.1025 \times 100 = 10.25\% $$ **Final answer:** The population increases by **10.25%** after two years.