Editing Accumulation function (section)

==Variable rate of return==
The [[Rate_of_return#Logarithmic_or_continuously_compounded_return|logarithmic or continuously compounded return]], sometimes called [[Compound interest#Force of interest|force of interest]], 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(t)= \exp \left( \int_0^t \delta_u\, du \right), </math>

reducing to

:<math>a(t)=e^{t \delta}</math>
for constant <math>\delta</math>.

The effective [[annual percentage rate]] at any time is:
:<math>  r(t) = e^{\delta_t} - 1</math>