Accumulation Function - Variable Rate of Return

Variable Rate of Return

The logarithmic or continuously compounded return, sometimes called force of interest, 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:

Read more about this topic:  Accumulation Function

Famous quotes containing the words variable, rate and/or return:

    There is not so variable a thing in nature as a lady’s head-dress.
    Joseph Addison (1672–1719)

    We honor motherhood with glowing sentimentality, but we don’t rate it high on the scale of creative occupations.
    Leontine Young (20th century)

    Adolescence is a time when children are supposed to move away from parents who are holding firm and protective behind them. When the parents disconnect, the children have no base to move away from or return to. They aren’t ready to face the world alone. With divorce, adolescents feel abandoned, and they are outraged at that abandonment. They are angry at both parents for letting them down. Often they feel that their parents broke the rules and so now they can too.
    Mary Pipher (20th century)