- 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 ininterest 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 :In the case of a positive
rate of return , as in the case of interest, the accumulation function is anincreasing function .Variable rate of return
The logarithmic or continuously compounded return is a function of time defined as follows:
:
which is the rate of change with time of the natural logarithm of the accumulation function.
Conversely:
:
reducing to
:for constant .
The effective
annual percentage rate at any time is::ee also
*
time value of money
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