A village has a population of 20,000. If the population grows at a rate of R% per annum, the population after T years is given by the formula P_T = P(1 + R/100)^T. a) Find the population after 2 years

Initial population, $P = 20000$
Annual growth rate, $R = 2\%$ (from the problem description)
Population after $T$ years, $P_T = 20808$

Substitute the given values:

Recognize that $1.0404 = (1.02)^2$.

Therefore, $T = 2$ years.

The population will be 20,808 after $\boxed{\text{2 years}}$.

Initial population, $P = 20000$
New annual growth rate, $R = 3\%$
Time, $T = 2$ years

Substitute the values:

Increase = Final population - Initial population
Increase = $P_T - P$
Increase = $21218 - 20000$
Increase = 1218

The population will be increased by $\boxed{1218}$.