Since I wrote about a simple formula for estimating your personal rate of return, someone asked whether the same formula works for multiple years as well. **The answer is yes and no.** It works well, provided that

- the net investments during the period are roughly even; and
- the beginning balance is large relative to the net investments

The simple formula doesn’t work well if these two conditions are not met.

After applying the simple formula, you get a *cumulative* return. You will have to annualize the result using this formula:

average annual return = (1 + cumulative return) ^ (1 / number of years) – 1

Here’s an example:

Beginning Balance 1/1/1998: $20,000

net investment in 1998: $1,000

net investment in 1999: $1,100

net investment in 2000: $1,200

net investment in 2001: $1,300

net investment in 2002: $1,400

net investment in 2003: $1,500

net investment in 2004: $1,600

net investment in 2005: $1,700

net investment in 2006: $1,800

Ending Balance 12/31/2006: $50,000

Total “net in” = $1,000 + $1,100 + … + $1,800 = $12,600

cumulative return = ($50,000 – 0.5 * $12,600) / ($20,000 + 0.5 * $12,600) – 1 = $43,700 / 26,300 – 1 = 66.2%

This means for this example, the *cumulative* return in 9 years from 1/1/1998 to 12/31/2006 is 66.2%. To convert it into an *annualized* number, you do:

average annual return = (1 + 66.2% ) ^ (1/9) – 1 = 5.8%

If I use the more precise XIRR method for this example, I get 6.0%. So 5.8% is close enough. But, if we have a different set of numbers,

Beginning Balance 1/1/1998: $2,000

net investment in 1998: $1,000

net investment in 1999: $1,100

net investment in 2000: $1,200

net investment in 2001: $1,300

net investment in 2002: $1,400

net investment in 2003: $1,500

net investment in 2004: $1,600

net investment in 2005: $1,700

net investment in 2006: $1,800

Ending Balance 12/31/2006: $25,000

Note the beginning balance of $2,000 is small relative to the net investments of $12,600. The simple formula gives the result of 9.4%, while the more precise XIRR method gives 11.0%. In this second example you are better off with the XIRR method because I think the 1.6% difference is too big.

Anonymous says

using your example, here’s what i thought.

profit is: 50,000 – (20,000 + 12,600) = 17400

therefore, cumulative return is:

17400 / (20,000 + 12,600) = 0.53

what’s wrong with this caluation?

Thanks. Great work.

TFB says

Calculate cumulative return using your “profit” number divided by beginning balance plus

one halfof your net investments.17400 / (20000 + 12600/2) = 0.662

The reason for one half is because your net new investments are put into the pool over time, not all at once at the beginning.

philip kassah says

What is my rate of return if I had an initial cost of $10,000.

Cash inflow

Year 1 3,000

year 2 4,000

Year 3 4,000

Year 4 2,000