The accumulation function a(t) is a function defined in terms of time t expressing the ratio of the value at time t (future value) and the initial investment (present value). It is used in interest theory.
Thus a(0)=1 and the value at time t is given by:
where the initial investment is k.
Variable rate of return
which is the rate of change with time of the natural logarithm of the accumulation function.
for constant .
The effective annual percentage rate at any time is: