Annual rate of return

dankelly79 · #1 Jul 3, 2007, 11:53 AM

How do I calculate annual rate of return for an account for which I have added deposits during the year? What formula should I use?

ebaines · Jul 4, 2007, 05:09 AM

A relatively straight forward way is to use the time value of each addition:

$ Average\ Return = \frac {Gain} {Average\ Daily\ Balance} $
A pretty good approximation of this is:
$ (Final\ Value - Initial\ Value - Add_1 - Add_2 ...)/(Initial\ Value + Add_1* Period_1 + Add_2*Period_2 + ...) $
Where $Period_i$ is the percentage of the year that $Add_i$ has been in the account.

While this is not exact, it's awfully close, especially if the magnitudes of the additional investments are relatively small compared to the original investment.

Here's an example:

If you start the year with $100, and add $25 each on March 31, June 30 and Sep 30, and the account finishes the year values at $225, the average return is approximately:

(225-100-25-25-25)/(100+.75*25 +.50*25 + .25*25) = $50/(100+18.75+12.5+6.25)
= $50/$137.5 = 0.3636

So, you made an average return of 36.4%.



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