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* <math>a(0)=1.</math>
* In the case that the accumulation is due to interest it is an [[increasing function]].
The [[Rate_of_return#Logarithmic_or_continuously_compounded_return|logarithmic or continuously compounded return]] is a function of time defined as follows:
:<math>\delta_{t}=\frac{a'(t)}{a(t)}\,</math>
which is the rate of change with time of the natural logarithm of the accumulation function.
Conversely:
:<math>a(n)=e^{\int_0^n \delta_t\, dt}\ ,</math>
==Common accumulation functions==
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