How much money do you need to retire with $150000 a year income

At their most self-indulgent, the theological scholars of the Renaissance were mocked for abandoning the debate over moral decisions to bicker about how many angels could dance on the head of a pin. The scholars of personal finance seem on track for a similar level of disconnection from reality.

Take this new study, in the Financial Analysts Journal, that says "retirement is not hopeless." Indeed, all you need to do is save 22 times the annual income you hope to have when you retire. That means if you make $150,000, and hope to retire on $100,000 a year, you only need to sock away $2.2m in a bank account to be able to retire comfortably.

The authors of the study assume you will live to be 100 years old, by the way, if not 105 years old. As you do.

The Wall Street Journal breezily calls this arrangement "retiring on your own terms."

You can call it retiring on your own terms, the same way you can call buying a private jet and a ranch in Telluride, Colorado living on your own terms – the terms, that is, of fantasy and not reality.

It's simply a math problem. Let's say you are in your 40s, making $150,000 a year, a generous salary in almost any city in the country. The taxman cometh, does he not? That $150,000, after taxes, becomes the slightly less dazzling sum of $100,000 a year.

It would be churlish to complain about such a salary, however: $100,000 a year is still far more than many Americans dream of, particularly in this less-than-stellar economy, and certainly at the upper end of the middle class.

Now you have to save that money as well as living on it. How much can you save? A standard and sensible budget, advocated by LearnVest and others, is to use a simple formula called 50/20/30. This means that you spend 50% of your salary on expenses. Another 30% goes to lifestyle expenses – the things that make life liveable unless you prefer living in a hut: cable and phone plans, clothes, books, gym fees, childcare and pets, restaurants and entertainment.

Then the final 20% goes to saving for retirement.

This is a reasonable budget. If you save more than 20% of your salary for retirement, you're giving up enjoying your present life: you're dedicating yourself to living in holy denial of all worldly pleasures like a monk or a nun, in the hopes of a lavish, or at least an exceedingly comfortable, life when you're over 60-years-old. Twenty percent for retirement is, by the way, an aggressive goal. Most people save much less.

So let's say that, with your net pay of $100,000 a year, you set aside 20% for retirement. That gives you $20,000 a year, saved, every year, to make your retirement as comfortable as possible. That's $20,000 a year you're now foregoing, not putting it into school fees, into trips, into anything you might need at the moment. It's locked away with a retirement chastity belt - in a bank account, by the way, not in stocks.

And once you reach this pinnacle of saving virtue, how long would it take you to reach your goal of $2.2mn for retirement?

Only a mere 110 years.

Yes, if you save $20,000 a year, you can expect to collect your $2.2mn in some future utopia, perhaps from the Starship Enterprise's ATM, which you will reach using your Jetsons jetpack. At that rate, you'll have had to make arrangements with science to keep your brain in a jar, pulsing for half a century past the normal mortality rate.

Ten years and a century seems a daunting amount of time to live past the age of 40, much less to save. So let's say you save more aggressively. How does 30% sound? You give up a few family vacations; your children go to community college.

If you save 30% of your salary, or 30% a year, it will take you 73 years to get to $2.2mn. Saving for 73 years is ambitious if most charts tell you you're lucky to live for another 40-50 years after your prime working years.

There are also a lot of impossible assumptions in this aggressive plan: for instance, that even if you reach $150,000 a year in annual salary, that you'll make it nearly forever, never suffering a layoff or taking less pay.

That's a far-fetched expectation. High salaries, as a rule, don't last forever. Older workers, particularly women between the ages of 45-54, are currently leaving the workforce in the greatest numbers, partly because there is no work for them. The salary of your prime earning years doesn't last very long.

Maybe you think this is all a bit severe. After all, can't you put your money in the stock market, where it can earn some returns?

You could - and earn 4% to 6% a year, conservatively, which would help you along.

But this plan doesn't trust the stock market. Ideally, your $2.2m would all be invested in "riskless assets" (no such thing, by the way; every investment carries some risk, even if low). In this case, the riskless asset that you should favor is a kind of Treasury bond that protect you against inflation. So far so good, except that no risk means no reward – which is why you should assume "a rate of return of zero".

That's where this gets completely out of hand. And yet the authors of the study imply that failing to achieve these incredible savings is a matter of mere discipline:

"Well-run … pension plans provided retirement income for generations. When plans failed, it is because they broke the rules. The same applies to individuals. By understanding a set of rules on how much to save and how to invest and then sticking to those rules – that is, by making a pension promise to oneself – retirement income goals can be met."

This is absurd.

This is why the cult of "saving for retirement" needs to be held in check, lest it brainwash anyone and pile guilt on hardworking families for having some mild enjoyment of life rather than living only for the future. Saving for retirement is a smart idea, and a necessary one, but stacking up bills in a bank account and eating ramen every night won't get you there; it is both utterly joyless and totally ineffective.

So what should you think about when you retire? There are libraries full of books about it. Start here: Retirement should include some thought to regular income – dividends, rental properties, insurance contracts – and a decent investment plan.

To be sure, there are some good things to take away from plan like this. The first is that people do tend to spend too much, and particularly with the rise of credit, they spend beyond their means. Household indebtedness has been a problem for years. One well-to-do techie, known as Mr Money Moustache, managed to sock away enough money to "retire" in his 30s with his family on $25,000 a year, which he considers a fortune. Even he has a lot of money in stocks and options, and says he makes sure to sell batches of them whenever he has to meet a major expense.

The other major issue: the retirement issue in this country is less due to personal failure than structural failures. Saving enough is not the primary problem with our retirement system. The primary problem is that wages have been dropping for decades, leaving people with much less to save - especially people who live on far, far less than $150,000 a year. That's largely because corporations are hoarding profits, raising CEO salaries and skimping on what they pay employees. Corporate executives have been the big beneficiaries of this trend, with a jump of 876% in pay between 1978 and 2011, as the New Yorker's James Surowiecki pointed out. At the same time, corporations – and the goverment – have largely reduced or eliminated pension plans that provided a retirement backstop to millions of middle-class employees.

If only we could impose the same kind of discipline on corporate executives as we do on the middle class, perhaps we'd have a real answer to the retirement problem.

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