Accumulation Function

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.

Examples:

  • simple interest:
  • compound interest:
  • simple discount:
  • compound discount:

In the case of a positive rate of return, as in the case of interest, the accumulation function is an increasing function.

Read more about Accumulation Function:  Variable Rate of Return

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