Edit: There’ve been some excellent comments on this post by people who understand more about the way compound interest is presented than I do. So perhaps the most important thing about this is that when people talk about averages, they may mean the arithmatic mean, or they may be talking about an average determined by the end result. Which can be two different things. Or you might just want to skip this post. I promise there are better ones. 🙂
We all know that when playing the market, even in safer categories like bonds and index funds and savings accounts, there’s some element of chance. The market fluctuates, and an average of 9.9% APY across 20 years might mean a sure thing or might mean wild jumps from 4% APY to 17% APY.
In the end, it’s ok because we weathered the storm and got our money, right? Well yes. Sort of. Being the spreadsheet geek I am and bored at work, I decided to put together a sheet which would illustrate the different possibilities.
What I came up with was one example of wild fluctuation, one of no fluctuation, one of mild fluctuation (less than 2% each way), and one of tiny fluctuation (0.5% each way). In each case, I put together some numbers rather randomly and then made changes until they all averaged the same 9.9%. Then I calculated what would happen if I put $1500 in an account and added $1000 more each year.
The results? Well, a steady 9.9% came out $66,537.96. The wildest one was $63,784.95, $2753, or 96% of the steady investment. The milder one was $65,947.12 (less than $1000 and 1% off). The tiny one actually came out ahead…by about $8.
Point being? It’s actually not that bad if it all averages out. While over $2500 may seem like a big difference for the wild one, it was only 4%, which isn’t too bad. I guess the lesson is that we can’t take compounding at face value and assume that an average of 9.9% means we have a certain amount of money. But we can come close. Food for thought next time you’re looking over a long-term account, such as a Roth.
(Note: the rubric for this is take the previous year, add it to the interest it would be earning and then add $1000. So, for example, for Year 2, the formula is add Year 1 and Year 1*Year 2’s interest and $1000. The assumption is that the $1000 would be added at the end, for simplification and that the balance of any year is its year-end balance.)