Understanding the time value of money
It's About Time
by Gary Foreman
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Does anyone think that $20,000 will buy a new car forty years from today? Maybe it's time for an article on the time value of money, accounting for inflation in long term investment plans, and related issues.
Lester was referring to an article that I had written saying that when you buy something today, you're agreeing not to buy something more expensive later. And, he's right. You can't simply take today's prices and expect them to be valid for future purchases, especially if you're looking more than a few years into the future.
The concept of rising prices is only one component of an economic theory called "the time value of money." It's a theory that we see every day but don't typically give any thought.
The basic statement of the time value of money is very simple. A dollar today is worth more than having one tomorrow (or next year).
Having money over a period of time is valuable. Money can earn more money. Suppose that you had $100 today and could earn 10% on it. A year from now you'd have $110. In two years $121. So having that $100 is valuable.
Also, I'd rather have $100 today than wait and get it tomorrow. I won't earn much interest in one day, but it should be worth a little more tomorrow. It's also safer getting it today. There's always that possibility, however small, that you won't get the money tomorrow. By getting it today, you've eliminated that risk.
Lester points out another area where the time value of money applies. That's in the area of retirement planning. Suppose that you expect to retire in 20 years. You know that prices will rise before then. But can you estimate by how much?
A quick and easy way to answer that question is to use the rule of 72. The formula is easy. The number of years in the future times the interest rate you expect equals 72. That's how long it will take for prices to double.
Let's do an example. You want to know how long it will take prices to double if inflation is 6%. A little algebra tells us that you divide 72 by 6. Prices will double in 12 years. So if you expect to retire in 20 years and inflation is 6%, prices will be nearly 4 times higher when you retire. ($1 x 2 = $2 in 12 years. That $2 x 2 = $4 the next 12 years. Or 4 times in 24 years)
If you play with the formula, you'll find that the rate of interest you choose makes a big difference in the results. For instance, 3% inflation would mean that prices would double every 24 years. Quite a difference compared to going up 4 times in the same amount of time.
You can use the same formula to calculate how long it will take your money to double in an investment account. For instance, if you're earning 9%, it will take 8 years (9 x 8 = 72).
You may want to get more precise than our little formula will allow. For that, you'll need something called a financial function calculator. It will do a lot more than time value of money, but it's easy enough to learn how to use it for time value questions. And, they're not expensive.
Some people will subtract the inflation rate from their investment return to get a "real" rate of return on their retirement savings. For instance, if you earned 8% on the money and inflation was 3%, you've really gained 5% in buying power.
Another application for time value of money is when you're trying to decide which payment plan you'd prefer. What happens if you were told that you could buy a car for $20,000 cash today. Or you could make $400 payments for 60 months. Or you could put $4,000 down and make $375 payments for 48 months.
You could add up all the checks you would write. And that would be a good rough estimate. But you'd get a more precise answer by using a calculator to bring everything back to today's dollars so that you'd have a fairer comparison.
Don't be intimidated by the concept. Just remember that having $1 today is more valuable that having one a year from now. And the same holds true if you're paying. A dollar that you pay today is more valuable than one that you'll pay next year.
With an understanding of the time value of money and the ability to use the rule of 72, you can help yourself in a variety of common money situations. Thanks to Lester for suggesting it.
Gary Foreman is a former financial planner and purchasing manager who founded The Dollar Stretcher.com website and newsletters in 1996. He's been featured in MSN Money, Yahoo Finance, Fox Business, The Nightly Business Report, US News Money and CreditCards.com. You can follow Gary on Twitter or visit Gary Foreman on Google+. Gary is also available for audio, video or print interviews. For more info see his media page.
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