TD - Compound interest- quiz-solution

QUESTION
Show that if you compound interest m times a year, with a quotes rate of f,
then an amount P invested at the beginning of the year grows to P(1+
r
m
)
m by
the end of that year. Hence show that after T years the investment has grown
to P(1+
r
m
)
mT
. Hence show that in the limit of continuous compounding the
investment grows as P exp(rT).
(Hint: limn→∞(1 +
1
n
)
n = e.)