I was reading from a book that if we compound annually at $40\%$ the rate of growth at any instant, such as $P$ in the following graphs (AL represents $1$ year) will be $40\%$ of the value at the beginning of the year. If we compound semi-annually the rate will be $40\%$ of the value at the beginning of the half-year in which $P$ lies etc
At this point I am confused because my understanding of annual compounding is that there is $1$ change in the original amount at the end of the year i.e. the graph (assuming $\$100$ at the start) should be:
I.e. no change until $L$ and a sudden jump in the graph at $L$
What am I misunderstanding here? I think it will be $\$140$ only at $L$ so $P$ should be $40\%$ of the beginning value only at $M$ and not earlier