Albert Einstein thought it was one of the great wonders of the world . You and I want it working for us, not against us.

The topic is compound interest, the subtle but incredible power of interest earned by interest, earned by interest. You can see its power in a simple rule of thumb, the rule of 72.  It’s a rough measure of the time it takes to double your money. Take the number 72 and divide it by your expected return. The result is the number of years it will take to double your money.

With common stocks returning 10 percent , it takes about 7 years to double your money. Drop the return to 7 percent and it takes 10 years. Increase the return to 14 and it takes only 5 years. Earn 14 percent rather than 7 and you’ll have 2 times as much at the end of 10 years, 4 times as much at twenty, and 8 times as much at the end of 30 years.

Einstein knew a wonder when he saw it.

Unfortunately, ordinary people don’t get to see compounding very easily. We measure things simply, in the here and now. Compounding is essentially invisible.

One of the most instructive ways to see the difference is to consider the impact of money management costs on your investments. If you own a mutual fund that invests in common stocks or have a personal money manager, you’re likely to pay 1.0 percent or 1.5 percent a year for the service. Since the return on common stocks is about 10 percent, the simple cost of management appears to be 10 to 15 percent of your probable return.

Not bad.

To put it in perspective, those are the two lowest rates on the IRS income tax tables. Few complain about taxes at that level. Affluent taxpayers are more likely to grimace because they pay at 33 and 35 percent rates.

In fact, the simple perspective understates the cost of management. It doesn’t consider the opportunity cost of lost compounding. You can understand this by going through a few calculations with me.

We’re going to find out the percentage of return that we lose to different management costs. We can do this by growing our initial investment at different rates of return and comparing the results.

If you invest \$10,000 for 25 years at a gross return of 10 percent, it will accumulate to \$108,347. But if the cost of managing the money is 2.0 percent, it will only grow to \$68,485. The \$39,862 difference was lost to management expenses. It amounts to 40.5 percent of our total return.

That’s higher than our highest tax bracket.

Now try a real world example. Suppose you’re paying 2.5 percent, as some do. Your accumulation will over the same period will be only \$60,983. Reduce your expenses to a reasonable 1.0 percent and your accumulation soars to \$86,231. From losing 48.2 percent of your return to expenses you now lose only 22.5 percent. The 25.7 percent difference is still a tax bracket that few Americans pay.