Investment Fees Over Time: What 1% Really Costs You

0:00The form: annual fee, 1% ▶

You have put it off for months, and today you finally open an investment account. The form is long, and near the bottom sits one line you almost skip. It says: annual fee, one percent of your account. Everyone agrees to that line, and almost nobody works out what it costs. One percent sounds like nothing, a penny on the dollar, so this time you do the sum in the margin. Say you put in a thousand dollars, once, and never add to it. A penny on every dollar comes to ten dollars a year. You plan to stay for thirty years, and thirty times ten is three hundred dollars. Three hundred dollars, and it buys thirty years of someone looking after your money. You write it down, tick the box, and the form moves on. But the sum in that margin is wrong, and not by a little. That one line will cost you more than six times your three hundred dollars. So what did your margin leave out? That one percent is charged on the whole account, whatever size it has reached. It is not charged on the thousand you started with.

1:21Level 1: $1,000, one year ▶

Level one: a thousand dollars, and a single year. Let the account grow seven percent a year, a round assumption and not a forecast. A year later, your thousand has grown by seventy dollars. Say the fee is that one percent, taken once a year, after the growth, on everything that is there. One percent of the grown account is ten dollars and seventy cents. The year earned you seventy dollars, and the fee took more than fifteen percent of that. In a year when the account falls, the fee is still taken, because it looks at the balance and not at the gain. And for all of this, no bill ever arrives; at most, the fee is a line on a statement. It is taken inside the account, so the balance simply grows a little less. One-time charges, like a sales commission, are a different sum; this is the percent that returns every year. Ten dollars and seventy cents: remember it, because it will not stay that small.

2:28Level 2: $10,000, thirty years of fees ▶

Level two: ten thousand dollars, and now the full thirty years. Your sum from the margin would say a hundred dollars a year, three thousand in all. Ten times the money means ten times the fee: a hundred and seven dollars in year one. But the account keeps growing, and the fee is one percent of whatever it has become. Guess, before the years run: what do thirty of those fees add up to? By year thirty, the fee for that single year is five hundred and sixty-nine dollars. That is far more than the first one, and the percent never changed. Add up all thirty, and you have paid about eighty-four hundred dollars. That is almost three times the sum in your margin. The percent stayed at one; what it was a percent of kept growing. And that is only what you paid, which is not yet what it cost you.

3:29Level 3: $100,000, the gap ▶

Level three: a hundred thousand dollars, the same seven percent, the same thirty years. First run it with no fee at all, which is a yardstick, not an offer. The account ends at seven hundred and sixty-one thousand dollars. Now run it with the one percent, and it ends a hundred and ninety-eight thousand dollars lower. But the fees you paid, ten times those of level two, add up to only about eighty-four thousand. Put every fee back on the pile, and you are still far short of the no-fee account. The gap is more than twice what you paid. Here is why: every dollar that left as a fee would have kept growing if it had stayed. The first fee alone, left in the account, would have grown to more than seven times its size. So what you paid and what you are short are not the same number. The difference was collected by no one, because it is growth that never happened. That is what your margin left out: a fee that grows with you, and growth the fee never let happen. Which leaves one question: how much of your money is that, and does a better market change it?

4:49The rule: what you keep ▶

Go back to a single year, and watch the order of things. Take any starting amount and call it P. After a year of growth you have a hundred and seven percent of it: one plus the growth rate, r. Then the fee takes one percent of that, so you keep ninety-nine percent: one minus the fee, f. So one year is P, times the growth, times what you keep. Thirty years is that same pair of steps, thirty times over. Multiplication does not care about order, so put all the growth on one side and what you keep on the other. On one side sits all the growth, which is exactly what you would have had with no fee. On the other side sits what you keep: one minus f, once for every year; call the years n. So what you end with, divided by what you would have had, is one minus f, to the power n. Look at what is missing from that line: the growth rate is gone, and so is the amount you started with. Four percent a year, or seven, or ten: one percent for thirty years leaves you the same share. Ninety-nine percent, kept thirty times in a row, leaves just under three quarters. Twenty-six percent of what you would have had is gone, about a quarter, at every level. Take the fee off the growth rate instead, as some guides do, and you get twenty-four and a half percent: still about a quarter.

6:20The check: your margin against the rule ▶

Now put the sum from your margin next to that rule. Three hundred on a thousand: your margin said thirty percent gone. The exact answer is twenty-six percent. So the margin had the share almost right, and the dollars six times too low: how can both be true? The quick sum runs a little high. Each year's one percent comes out of an account that earlier fees have already made smaller. Over ten years the quick sum is nearly exact, and the longer you stay, the wider it runs. So the thirty percent was close; the mistake was what you took it from. You took it from the thousand you put in. The fee takes its share from what the thousand would have become, more than seven times as much. A share a little too high, of an amount more than seven times too small: there are your six times.

7:19What people actually pay ▶

One percent was an assumption, so what do people actually pay? The fee goes by many names: an expense ratio on a fund, an advisory fee, plan fees in a retirement account. Inside a fund, it pays for managing the money, for marketing and for paperwork. Across American funds, Morningstar's fee study puts the average cost, weighted by where the money sits, at about a third of a percent a year. Over thirty years, a third of a percent takes about nine percent of what you would have had. An advisor's fee comes on top of the fund's own costs, and it is often around one percent. With both, thirty years take about thirty-three percent of what you would have had. The rule is the same each time: one minus the fee, to the power of the years. One level is left, and it is the one where one percent stops sounding small.

8:21Level 4: $1,000,000 ▶

Level four, the last one: a million dollars. In the very first year, the fee is ten thousand seven hundred dollars. Nobody would skip that line on a form. Yet it is the same line, the same one percent, taken in the same quiet way. Run the thirty years, once with the fee and once without. At the end, you are almost two million dollars short, and no statement will ever tell you. Almost two million, on the million you put in. Now look back down the ladder, because every level tells the same story. With one deposit, seven percent growth and thirty years, one percent a year costs about twice what you put in.

9:11Back to the form ▶

So go back to the form, and to the sum in the margin. Cross out the three hundred dollars, and write what the line costs: almost two thousand, on your thousand. Three things were hiding in that one percent. It is a percent of everything, not of the gains. It grows as the account grows, so thirty fees are far more than thirty times the first. And each fee takes its future growth with it, which no bill will ever show. To make up for the fee, the account would have to earn about eight point one percent a year instead of seven. Almost every guide ends here with advice about what to buy; this channel stops at the sum. One percent on a form now reads differently to you: a percent of everything, every single year. One minus the fee, once for every year you stay, and that's the math behind the money.

10:10What's next ▶

Next time: an account goes up sixty percent, then down forty, averages plus ten percent a year, and still loses money. Before you go: what did you guess the thirty years of fees would add up to? I'm the MoneyMathician, and if you subscribe, the next one will find you. Until then: do the math!