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# Investment Performance Calculator

This calculator shows you how your portfolio is doing. Just give it your investment’s beginning and ending balance for a given time period, and any additions and withdrawals (including dividends not kept in the account) along the way.

## How Does it Work?

This calculator can only give you an estimate (total accuracy would require you to give the date and amount of each addition and withdrawal) but it’s a *respected* estimate, using a formula recommended by *The Four Pillars of Investing* and The Motley Fool, and widely used by many others.

Let’s take a couple of examples to see how the method works.

**Example 1:** First, assume your account grows from $1000 to $1200 in one year, and that you don’t make any additions or withdrawals during that time. That means your investments created $200 of wealth, which is 20% of the $1000 it had to work with – so the return rate must be twenty percent.

**Example 2:** Now for a more complicated example. Again assume that your starting balance was $1000 and your ending balance was $1200, but that you made a $50 addition at some point during the year. This time, your investments only created $150 of new wealth. To turn that dollar figure into a percent, you have to decide “a percent *of what?*” – that is, how much money did the account have to work on during the year? Well, it had the initial $1000 for the whole year, and the $50 addition for some unknown portion of the year, so we’ll use the estimate that it had the equivalent of $1025 for the whole year (that is, the whole thousand, plus half of the fifty). Now the growth rate is

($150 growth) / ($1025 estimated average principal) = 0.1463

or 14.63 percent.

See below (or one of the two links above) for a formula that you can write down or use in a spreadsheet. (You may have to do a little painful thinking to convince yourself that the formula really does come out of the logic described here.)

## Investment Return Formula

The estimate used in Example 2 is that

$1025 grew by $150

Equivalently (but more confusingly!)

where B_{start} and B_{end} are the starting and ending balances, and N is the net additions minus withdrawals. Plugging these values into the return rate formula gives:

where Y is the elapsed time, in years.

**BUG FIX:** The last formula shown was wrong before 9/26/2014. (The calculator was correct.) Apologies for the confusion.