Calculating population size at any future time If current population size is $P$ and average life-time of any member is $L$. Any pair of member of the population is allowed to have $C$ children on an average. They can have children between the age of $A$ to $B$.Then how can I tell population size at any  future time?
 A: Ross has given you a formula for the first $A$ years.  Beyond that you could model this, or as an approximation assume that the shape of the population distribution does not change, in which case you will get exponential population change.
For simplification, let's assume everybody lives exactly $L$ years and each person gives birth to $C/2$ children (or that the half of them that are female each give birth to $C$)   after exactly $A$ years.  We want to find $k$ where the population after $N$ years is $Pk^N$.  The shape of the population distribution will be a truncated exponential or geometric distribution with each year group having $k$ times as many people as the one a year older, so the number dying each year will be $P\dfrac{k^N-k^{N-1}}{k^L-1}$ and the number being born  $Pk^{L}\dfrac{k^N-k^{N-1}}{k^L-1}$.  But the number being born is also $\dfrac{C}{2}Pk^{L-A}\dfrac{k^N-k^{N-1}}{k^L-1}$ so $k=\left(\dfrac{C}{2}\right)^{1/A}$ and that means that the population after $N$ years is 
$$P\left(\frac{C}{2}\right)^{N/A}.$$
This seems fairly intuitive: note that it suggests that earlier parental age at childbirth means faster population growth (or decline) even if lifetime fertility stays the same, and that the population will grow iff $C>2$. 
To make this more sophisticated, you can introduce $B$, so childbirth takes place over an interval (this will affect the denominator of the exponent, putting it between $A$ and $B$), and you can also widen the distribution of death with substantial effects if it is possible to die before childbearing age $A$ and the average number of children per couple does not take this into account. You could also start with a different population shape, or allow random effects, or allow fertility to vary over time, in a not particularly complicated model.
A: Though this is still not a well-specified problem, here are some thoughts.  You start with $\frac{P}{L}$ people of each age, which will be strange as the distribution will not stay uniform.  If the childbearing is random over the span, you will have $\frac{3PL}{2(B-A)}$ children born in the first year and $\frac{P}{L}$ die.  These numbers will hold for $A$ years so you will have $P+\left(\frac{CPL}{2(B-A)}-\frac{P}{L}\right)N$ in year $N$
