BOSTON » John C. "Jack" Bogle is preoccupied with numbers. At 81, an age when most of us can only hope to be so sharp, the founder of mutual fund company Vanguard Group rattles off data point after data point.

How much have investors earned in the stock market over the past century? About 9 percent a year. How much of that came from dividend income? About half, with the rest coming from earnings growth that drives stock prices, Bogle says.

The problem is those numbers don’t tell the whole story. Investment fees, sales charges and trading costs can eat up much of that return — as much as 75 percent, Bogle says, not counting taxes.

It’s an example of how numbers are twisted in a way that skews reality and leads to false expectations. Those are "the perils of numeracy" that Bogle warns about in his latest book, such as beliefs that stocks will keep delivering the level of returns they have in the past.

"Numbers don’t necessarily repeat themselves, and the person who presents the number to you may have a vested interest," Bogle says. "If people fall for the idea that there’s certainty in numbers, they’re making a big mistake."

Bogle’s ninth book is a collection of his writing over the past decade. It’s more than 580 pages, and its title is also long: "Don’t Count on It! Reflections on Investment Illusions, Capitalism, ‘Mutual’ Funds, Indexing, Entrepreneurship, Idealism and Heroes."

Bogle has become a hero to many because of his founding of Vanguard, the largest U.S. mutual fund company with nearly $1.5 trillion in U.S. fund assets. It was Bogle who launched the Vanguard 500 Index Fund, the first index mutual fund, in 1975. Index funds track segments of the market like the Standard & Poor’s 500 and thereby aim to match performance.

They’re a low-cost alternative to actively managed funds meant to beat the market.

Although Bogle stepped down as Vanguard’s senior chairman some 10 years ago, he remains a force in the fund industry. Here are excerpts from a recent interview:

QUESTION: You have consistently argued that index funds will always produce better long-term returns than actively managed funds. Yet a few active managers — Bruce Berkowitz of Fairholme Fund is a recent example — consistently beat the market. Wouldn’t investors be better off going with those select funds?

ANSWER: There is always a manager out there who is going to do well. From what I can see, Berkowitz seems like an intelligent manager, and he has done well. (Editor’s note: Fairholme Fund has delivered an average annual return of 11.6 percent over the past 10 years, while the S&P 500 has been essentially flat.)

But investors who start out in their 20s today could end up investing for 70 years, since people are living longer. Well, Bruce Berkowitz is not going to be around managing funds 70 years from now.

If you start with four stock funds when you’re young, you may end up with 70 managers running them over your investing lifetime, since managers typically change every five years or so. And there is no possibility at all that they can beat the index.

Even Berkowitz might run into trouble and make some bad moves. It’s one of those cases where even the best generals make mistakes.

Q: What’s your current outlook on the stock market?

A: The market is at a relatively fair value now but may be a bit overvalued for the long term. But I would no more predict what will happen in 2011 than fly to the moon.

Anybody who goes into the market to make money specifically in 2011 should either be spanked or have their head examined. It’s just too short of a period to predict, and it’s a crap shoot.

Q: What about for the long term?

A: I expect stocks will have a dividend yield of about 2 percent, with stock price appreciation of maybe 6 percent from earnings growth. So you might see a total return of around 7 to 8 percent. For bonds I expect around 3.5 percent.

With compound interest, stocks could double in the next decade, and bonds will go up about 50 percent.

Q: What worries you most about the markets?

A: I’ve never seen a more difficult time to invest, with the specter of these enormous deficits hanging over us and with the global economy teetering a great deal more than people think it is. China poses special risks, with a huge construction boom that can’t go on forever.

Q: Many investors have been adding more international investments, expecting better growth. Do you think that’s smart?

A: If you invest in a diversified international fund, your largest investment will be in Japan, which doesn’t look so good to me now. And your second largest will be in Britain, which is in worse shape than the U.S. Your third-largest investment will be in France, where they don’t want to seem to work anymore. I don’t see any great attractiveness to that.

I think the message should be, "Stick with the U.S. and add an international component to your portfolio if you want it."

Q: You keep an active schedule at 81. Will you slow down?

A: I’m definitely slowing down, doing less travel and less speaking, deliberately.

But I still have a huge amount of energy and a strong voice. And I think, honest to God, the world really needs somebody to say, "I see what you are doing, and I think there is a better way." I think there ought to always be someone who says, "I think this system can be fixed, made better, for investors."