Calculating Rate of Growth without a Population
The breeding lifespan of an individual is (maximum life span $L$ - age of sexual maturity $M$).
Call the time between pregnancies $\tau$ and the gestation period $g$. Then the average number of pregnancies per (female) individual is then $(L-M)/(\tau+g)$.
If the average number of individuals per pregnancy is $N$, then each reproducing individual produces $N(L-M)/(\tau+g)$ offspring in their lifetime.


If this species has males and females (gonochoric/dioecious), and a 50/50 sex ratio, then the number of females per female is $N(L-M)/(2(\tau+g))$.

This is a growth rate per generation: the generation time is approximately (mean time between birth of mother and birth of offspring) = $(M+(L-M)/2)$ (it's a little more complicated than this); the growth rate per unit time would be approximately equal to the ratio (growth rate per generation)/(generation time). 

Other things you might need to take into account: survival of juveniles up to $M$; menopause (unusual).