One of my favourite TV shows is the PBS documentary series *Frontline*. Last week's episode – *The Retirement Gamble* – is a must-see for every investor, particularly the segment on how fees can devour returns.

*Frontline* interviewed index fund pioneer John Bogle, who compared the performance of two hypothetical equity portfolios – one earning 7 per cent, and the other earning 5 per cent (7 per cent less 2 per cent in fees).

Two per cent may not seem like much in any given year. But over a long time period, the impact is enormous: Assuming a 50-year horizon, the second portfolio would have lost 63 per cent of its potential returns to fees, Mr. Bogle said.

"What happens in the fund business is that the magic of compounding returns is overwhelmed by the tyranny of compounding costs. It's a mathematical fact," he explained.

If you're having trouble comprehending how 2 per cent in fees can destroy nearly two-thirds of your returns, read on. Today we're going to pick up where Mr. Bogle left off and explore the math in more detail. You can play along by using an online compounding calculator like the one at http://tinyurl.com/46syn.

Okay, let's assume there are two investors: Investor No. 1 owns a portfolio of stocks worth $100,000, pays no ongoing fees (apart from commissions when he purchased his shares) and earns the market return of 7 per cent annually. Investor No. 2 owns the same stocks in a mutual fund that charges 2 per cent in fees, and he therefore earns a return of 5 per cent.

Now fire up your compounding calculator, because the fun is about to begin. For Investor No. 1, in the box labelled "current principal," enter $100,000. Leave the next box, labelled "annual addition," blank, because we'll assume he doesn't make any additional contributions.

Now, in the "years to grow" box, enter 50, and for "interest rate," enter 7. In the next box, make sure the calculator is set to "compound interest 1 time(s) annually." Finally, hit "calculate."

If you've done everything right, you should see a "future value" of $2,945,702.51. This is what Investor No. 1 would end up with after 50 years at a growth rate of 7 per cent. To figure out his return, subtract the original $100,000, which gives you $2,845,702.51.

Now do the same for Investor No. 2. The only number you need to change is the interest rate, which is now 5 per cent. Hit "calculate," and you'll get a future value of $1,146,739.98, for a return of $1,046,739.98.

You'll notice that Investor No. 2's return is less than half of Investor No. 1's. In fact, consistent with Mr. Bogle's example, Investor No. 2 made about 63 per cent less than Investor No. 1 – and all because of just 2 per cent in fees charged every year.

Here's something else to consider: The longer the time horizon, the bigger the bite that fees take. Taking our example a step further, after 60 years, fees would eat up 69 per cent of returns. After 100 years, 85 per cent. Nobody invests for that long, of course, but you can see the trend here: As the time horizon approaches infinity, the proportion of returns eaten up by fees approaches 100 per cent.

Why does this happen? Because, over extremely long time periods, even small differences in compounding rates have a gigantic impact on returns.

Also note that Investor No. 2's fees increase over time. In the first year, he pays about $2,000 in fees (2 per cent of $100,000). In the second year, because his portfolio has grown to $105,000, he pays about $2,100 in fees. In the third year, $2,205. And so on. This is money that could otherwise be compounding in his favour.

Fees are the silent killers of investment returns. Don't make the mistake of thinking a couple of percentage points don't matter – in the long run, they're huge.