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 . 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): * simple interest: * compound interest: * : * :