[jpullen]

If I have a beginning balance uneven yearly contributions and a ending balance how do I calculate an annualized rate of return?

[shaneshot417]

Don't quote me on this because it has been a long time since high school. Take ending balance, subtract money invested to get profit. Divide profit by money invested. That give you percent of return. Example invest 3000. Now, subtract it from total worth at end of term, suppose it to be 5000. Then take profit and divide it by original investment . That equals percent of return. . 66666 percent. Something like that...

[ArcSine]

Shane's calc works fine for a single investment with a one-year horizon. But the wording of the question suggests a multi-year scenario, with an uneven pattern of annual contributions into the investment.

JPullen, if (1) you're given an opening balance of B; (2) you know the subsequent contribution amounts (not necessarily the same) and the timing of each, in terms of the number of one-year periods between the contribution and the ending date; and (3) you're given the ending amount E; then your answer is the amount r which solves a basic forward-value equation.

Short example: Opening balance is B; a contribution is made after 2 years; another is made after 4 years; and the result is an ending balance E one year after the final contribution; then



The effective average annual return r which makes the opening balance and the two subsequent contributions grow to E by the end of the fifth year is what you're looking for. Finding r, I'm afraid, requires plain ol' trial-and-error. (Or at least the modern equivalent, such as Excel's Goal Seek, WolframAlpha... )