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 ladys head-dress.”
—Joseph Addison (16721719)
“I dont know but a book in a mans brain is better off than a book bound in calfat any rate it is safer from criticism. And taking a book off the brain, is akin to the ticklish & dangerous business of taking an old painting off a panelyou have to scrape off the whole brain in order to get at it with due safety& even then, the painting may not be worth the trouble.”
—Herman Melville (18191891)
“Compassion is frequently a sense of our own misfortunes, in those of other men; it is an ingenious foresight of the disasters that may fall upon us hereafter. We relieve others, that they may return the like when our occasions call for it; and the good offices we do them are, in strict speaking, so many kindnesses done to ourselves beforehand.”
—François, Duc De La Rochefoucauld (16131680)