Money math you need to know

By Liz Pulliam Weston

In "9 money rules to live by," I listed the economic and financial concepts I thought everybody should know.

In "16 favorite money rules of thumb," I gave you some rough guidelines for figuring out how much to save for retirement, borrow for homes and spend on cars, among other things.

The first column was essentially Economics 101. I covered ideas such as opportunity cost and the hedonic treadmill that might sound pretty esoteric but actually have profound effects on our daily lives.

The second column was born from all the "just give me the answer" pleas I get from readers for simple guidelines they could use to manage their money.

Now I'm going to round out the trilogy by teaching you some math tricks you can use to get a handle on your investments, calculate the cost or benefit of a financial move and impress your friends at parties.

None of these tricks requires more than simple arithmetic (addition, subtraction, division and multiplication), and some of them you can do in your head. Some are so simple they can be explained in a few sentences; if it takes longer and you're in a hurry, you can read the last paragraph of each section to get the rule of thumb.

The rule of 72

Need a quick way to estimate how long it will take for your money to double at a given rate of return?

Divide the return into 72. So if you're averaging an 8% annual return, it will take you nine years to double your money (72 divided by 8 equals 9).

The rule of 70

Inflation erodes the buying power of a dollar, so that eventually it will buy only half of what it used to.

Want to know how quickly your money will lose half its buying power? Divide 70 by the expected inflation rate. If it's 3.5%, your dollar will be worth 50 cents in 20 years (70 divided by 3.5 equals 20). If inflation soars to 10%, your money's value is halved in seven years.

Understand the value of compounding

It's been called the Eighth Wonder of the World, but many people still don't grasp how amazingly investment returns can add up over time.

One way to dramatically illustrate the point is to use the example of the doubling penny. If I give you a penny at the start of the month and promise to double it every day, you'll have $10.7 million after 30 days.

Of course, you're not going to double your money every day or even every year. But 8% or 9% is a reasonable rate of return to expect over the long run on a diversified portfolio of stocks, bonds and cash, so doubling your money every eight or nine years (remember the rule of 72) is well within the range of possibility.

The following chart demonstrates how quickly a $100 investment can grow given different interest rates and time periods.

How $100 can grow

After:	6%	8%	10%
10 years	$179	$216	$259
20 years	$320	$466	$673
30 years	$574	$1,006	$1,745
40 years	$1,028	$2,172	$4,525

This chart can be used the other way around to illustrate future gains you lose when you aren't invested. If you withdraw $100 from a retirement account at age 25, for example, you're giving up more than $2,000 of future retirement money, assuming 8% average annual returns over the next 40 years.

Here's a way to further boil it down: Every dollar you invest can grow to $2 in 10 years, $5 in 20 years, $10 in 30 years and $20 in 40 years, assuming an 8% average annual return.

What's your time worth?

If you work, you need to understand the basic concept that you're trading your time (a nonrenewable resource) for money. So when you buy something, you're trading minutes or hours or days of your life to procure that thing.

One way to do that is to simply look at your hourly wage. If you make $20 an hour and something costs $40, you can figure that it takes two hours of your life to pay for that thing. (A fast way to estimate your hourly wage if you're salaried: Knock off the last three zeros and halve the result, so $50,000 becomes $50, which halved is $25. The rate you get will be a bit high but in the ballpark.)

Continued: Don't forget about taxes

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