数学不好,财务吃亏

转自华尔街日报
http://chinese.wsj.com/gb/20080117/inv153057.asp?source=UpColumn

许，我们的问题只是数学水平太差了。 Maybe we're just lousy at math.

官方储蓄率依然顽固地保持在几近于零的水平，截止9月份的12个月中，抵押贷款和消费贷款增长了7.4%，而Pew Research Center最近发布报道称，半数美国人对自己的个人财务状况的评价是“一般”或“糟糕”。

人们很容易将这一切归咎于理财不善。但想想是不是还有另一个原因：我们的数学能力低下。让我们来看一看是哪里出了问题，又该如何做得更好。

──损失利息。在最近的一项研究中，市场营销教授埃里克•爱森斯坦(Eric Eisenstein)和斯蒂芬•霍克(Stephen Hoch)发现，大多数人都低估了储蓄的增值空间和借贷的最终成本。

问题是：人们是按单一利率而非复利计算。比如说，如果我们的投资以每年8%的利率保持十年，我们的收益并非许多人想的那样为80%。

确切地说，我们的累计收益将会是116%。记住，我们不仅会从最初的投资上获得利息，早期的投资收益也会生息。同样，对于信用卡欠款，我们要为最初买东西的钱支付利息，还要为遗留下来的尚未支付的利息掏腰包。

任教于康奈尔大学(Cornell University)约翰逊管理学院(Johnson Graduate School of Management)的爱森斯坦教授说：“人们使用单一利率计算是因为他们不知道别的方法。利率越高、时间范围越长，错得就越离谱。”他指出，这个基本 的数学错误解释了人们为什么迟迟不愿为退休储存积蓄，以及为什么老是推迟还清信用卡欠款。

──推测错误。给我们下绊子的不光是信用卡。达 特茅斯学院(Dartmouth College)的经济学教授维克托•斯坦戈(Victor Stango)和乔纳森•辛曼(Jonathan Zinman)的新研究发现，我们没有意识到，自己为那些所谓的“低月供”贷款付了多少利息。

这两位作者分析了美国联邦储备委员会(Fed) 1983年消费者财务知识调查的数据。在那次调查中，消费者需要回答这样的问题：如果他们贷了1000美元买家具，分期12个月偿还，他们愿意最终总共还多少钱。

一些人回答1200美元，这意味着实际利率应该是35%。然而，当消费者被问及这个还款额对应的利率是多少时，98%的人都低估了。

每月还款额越低，我们就越有可能低估利率。为什么？我们做心算的时候，忽视了这样一个事实：每个月的还款都是在减少贷款余额。在短期贷款的情况下，每月还款额中的一大块都是本金还款。

达特茅斯学院塔克商学院(Tuck School of Business)的斯坦戈教授说：“我们明白这些问题很难。人们会得出错误的答案也不稀奇。稀奇的是人们犯的错误总是同样的方向。他们低估储蓄的好处，同时低估举债的代价。”

──做得更好。我们该如何避免这些错误呢？试试以下三个策略：

──如果你想申请“低月供”贷款，问问贷款机构，按年的服务费费率是多少。那会让你明白月供到底是低还是高。

斯坦戈说：“人们不敢问强硬的问题。他们担心贷款会因此不被批准。他们不想让自己显得无知。”

──要想把握住借贷的成本和储蓄的收益，可以试试一些在线的金融计算器。www.dinkytown.com上有许多此类计算器。

──当你权衡是花还是存的时候，记住72定律。用72除以你预计的投资回报率，就能算出让你的钱翻一倍需要多长时间。

你估计每年的收益率能达到7%？用这个数字除72，就会知道，让你的钱增加一倍需要10.2年。其中的意义在于：如果你存了1000美元，十年以后你就会有大约2000美元，20年以后就是4000美元──而30年以后就会变成8000美元的“巨款”。

Jonathan Clements

（编者按：本文作者Jonathan Clements是《华尔街日报》个人理财专栏“Getting Going”的专栏作家）

 Maybe we're just lousy at math.

The official savings rate remains stubbornly close to zero, mortgage and consumer debt leapt 7.4% in the 12 months through September, and the Pew Research Center recently reported that half of Americans rate their personal finances as fair or poor.

It's tempting to blame all this on financial recklessness. But consider another culprit: Our feeble math skills. Here's a look at where we go wrong -- and how we can do better.

-- Losing interest. In a recent study, marketing professors Eric Eisenstein and Stephen Hoch found that most folks underestimated how much savings would grow and how much debt would end up costing.

The problem: People think in terms of simple interest, not compound interest. For instance, if our investments clock 8% a year for 10 years, we don't earn 80%, as many people assume.

Rather, we would notch a cumulative 116%. Remember, we earn interest not only on our original investment, but also on the investment gains earned in earlier years. Similarly, with credit-card debt, we pay interest both on our original purchases and on any monthly interest charges we didn't pay off in full.

'People use simple interest because they don't know to use anything else,' says Prof. Eisenstein, of Cornell University's Johnson Graduate School of Management. 'The higher the interest rate and the longer the time horizon, the worse the error.' He argues that this basic math mistake helps explain why people delay saving for retirement and why they postpone paying off credit-card debt.

-- Guessing wrong. It isn't just credit cards that trip us up. We also don't appreciate how much interest we're paying on loans that promise 'low monthly payments,' according to new research by Dartmouth College economics professors Victor Stango and Jonathan Zinman.

The two authors analyzed data from the Federal Reserve's 1983 Survey of Consumer Finances. For that survey, consumers were asked how much they would expect to repay in total, assuming 12 monthly payments, if they took out a $1,000 one-year loan to buy furniture.

In response, folks gave answers such as $1,200, which means the effective interest rate was 35%. Yet, when consumers were asked what interest rate was implied, 98% underestimated the rate.

The fewer the number of monthly payments, the more we're likely to underestimate the interest rate charged. Why? When we do our mental calculation, we overlook the fact that, with each monthly payment, we're reducing the loan balance. With a short-term loan, these principal repayments are a big chunk of each monthly payment.

'We know these are hard problems,' says Prof. Stango, of Dartmouth's Tuck School of Business. 'It isn't surprising that people get the answers wrong. What's really surprising is that people are almost always wrong in the same direction. They underestimate the benefits of saving and they underestimate the costs of borrowing.'

-- Getting better. What can we do to avoid these mistakes? Try these three strategies:

-- If you're considering a loan with 'low monthly payments,' ask the lender what the finance charge is as an annual percentage rate. That will tell you whether the monthly payments are truly low.

'People are scared to ask the tough questions,' Prof. Stango says. 'They're worried about not getting approved for the loan. They don't want to seem naive.'

-- To get a handle on the costs of borrowing and the benefits of saving, try playing around with some online financial calculators. You can find a great collection of calculators at www.dinkytown.com.

-- As you toy with whether to spend or save, keep in mind the rule of 72. If you divide 72 by the rate of return you expect to earn, that will tell you how long it takes to double your money.

Think you can earn 7% a year? Divide that into 72, and you will learn that doubling your money takes 10.2 years. The implication: If you saved $1,000, rather than spending it, you would have roughly $2,000 after 10 years, $4,000 after 20 years -- and an impressive $8,000 after 30 years.

 

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