The accumulation functiona(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
For various interest-accumulation protocols, the accumulation function is as follows (with i denoting the interest rate and d denoting the discount rate):