John Bogle, founder of the Vanguard Group, recently explained the unavoidable mathematical reason why passive wins over active in retirement investing: You keep more of your own money invested, and it compounds in your favor, not Wall Street's.

Fees paid to active managers end up equaling a huge amount of lost return, up to 80% of your gains over a lifetime, Bogle said. Don't believe it? You ignore such "humble arithmetic" at great risk.

Bogle spoke at length in an interview with Bloomberg News, predicting future pension returns of 5% before fees, not the 8% many assume. The return on bonds is 3% and the return on stocks, dividends included, is around 7%, Bogle said. "We aren't going to get 8% a year in the next eight to 10 years," he said.

Interestingly, my MarketWatch colleague Alicia Munnell of the Center for Retirement Research at Boston College found Bogle's "scary math" showing up in real 401(k) and IRA plans: Put in $1 and over the long run you kept 27 cents.

Now, the reason the math matches up isn't entirely fees, as Munnell points out. Some people fail to contribute consistently, and there are "leaks" in plans that cause money to leave, such as inopportune borrowing against your own retirement or taking money out early, thus triggering hefty penalties and taxes.

Still, the amount saved should be higher than the dollars set aside plus the compounding market return — much higher — and it just isn't. The typical worker saving diligently since 1982 should have had $373,000 in a qualified plan by age 60. Instead, that saver has $100,000, Munnell found.

An awful deal

Where did the money go, and what can you do to avoid being that person? Clearly, you can avoid borrowing against your own savings. And you can make sure to contribute steadily and to the maximum possible, especially in the early years to give compounding a chance to help you along. More time equals more money.

And, as Bogle explains, you can dramatically cut Wall Street's take by using index funds. About a third of investors do so now, and that number is likely to rise over time as people realize how awful a deal active management is for retirement savers.

The reason is compounding: Invest a dollar in the markets and you stand a chance to earn, charitably, 7% on your money. But the manager is taking 2% of your total plan balance of $1.07. So while you might make 7 cents on the dollar, the adviser is sucking in a bit more than 2.1 cents. In reality, that 2.1 cents is more than 30% of your one-year gain of 7 cents.

That giant sucking sound continues as your balance grows. Imagine instead of $1 you have $100,000 in your IRA in your 40s. You should be well on your way to retirement with that kind of balance, assuming you have a decade or two of earning years left.

Overwhelmed

Yet the active manager is still charging 2%. If you do earn a nice 7% on your pot, you pull in $7,000. Yet you're giving $2,140 to the manager. That's right, you are still losing nearly a third of your money to Wall Street.

All along the way, it must be assumed, the manager is earning a compounding return on your money, money that he or she keeps and will never share with you.

As that money compounds outside of your plan it overwhelms your results. Over the long haul the amount of your potential return lost to Wall Street is more like 65% and rapidly heading higher.

In short, every dollar you give away to active managers is gone forever and compounding for someone else. Retiring with more means you have to plug that gap by lowering fees, as soon as possible and permanently.