Philip Moeller is that rare person who gets two streams of income from Social Security. Like millions of other older Americans, he gets a monthly benefit. But he also gets an additional income stream from the unlikely best-seller he co-authored, "Get What's Yours: The Secrets to Maxing Out Your Social Security."

That book's runaway success—it spent 25 weeks on the New York Times bestseller list—got Moeller, 70, thinking about another complex and crucial government safety-net program: Medicare. His new book, Get What's Yours for Medicare: Maximize Your Coverage, Minimize Your Costs, comes out on Tuesday.

Bloomberg spoke with Moeller about how to get the most out of your Medicare dollars, and why it's smart for even very affluent Americans to enroll. The interview was lightly edited for space and clarity.

Q. Is Social Security, the book, going to make you rich?

A. If I live a really long time, that might be true. The book is an annuity that I hope will pay a modest return for a very long number of years.

I waited to claim Social Security until I was 70, and my benefits are going to be really nice for the rest of of my life. My wife will do the same thing. She's 66 but got grandfathered in the new law that ended the ability to use a strategy called "file and suspend" that we wrote about in the book.  [One of Moeller's co-authors, Boston University economist Larry Kotlikoff, estimated that the strategy could add $50,000 to a couple's lifetime benefits.] Larry was told by people within Social Security that the book was responsible for changing the law about the claiming technique, which we're not terribly proud of.

Q. You'd think affluent people wouldn't use Medicare, since they have better options and the money to get health care outside the program. Is that true?

A. Smart, affluent people should absolutely use Medicare as a vehicle to protect assets. Heath-care expenses are the biggest uncontrolled expense that most older Americans have in their lives. The average lifetime out-of-pocket for an average American is about $250,000—but that is an average. Having a lot of money skews that average, because wealthier people invariably spend more on health care, because they can afford it and have higher out-of-pocket expenses.

I have a good friend who became very wealthy and retired in his early fifties. For the last 20 years, he's lived a wonderful, affluent lifestyle. He can afford to self-insure his health care, but he doesn't. He has Medicare, because it saves him a tremendous amount of money. Until recently, he didn't have a Medicare Part D drug plan because he didn't take any expensive medications, so figured he didn't need it. He's now recognized that the drug coverage is a wonderful catastrophic insurance policy against these very wonderful but very expensive new medications that odds are more and more of us will need to take when we get old.

He signed up for Part D but was five years late in enrolling, so has to pay like a 50 percent premium penalty for the rest of his life. That's the nature of Medicare penalties when you're late in enrolling.