Compound interest in numbers: what 1 percent really costs

Transcript

10,000 euros, seven percent a year, nothing added, nothing taken out. After 30 years you have about 76,000 euros. And here is the part almost nobody expects: in the ten years after that, more than 73,000 are added. The last ten years bring more than the first thirty combined. I'm Peter, and today we do the math. Four examples with charts: compound interest, costs, extra return and losses.

Why is that? Because your money earns returns not only on the starting amount but also on all the gains before. A simple rule of thumb: divide 72 by the yearly return, and you know roughly how long it takes for your money to double. At seven percent, that is just over ten years. 10,000 becomes 20,000, then 40,000, then 80,000. Every doubling is bigger than all the ones before combined. That is why the most important ingredient of compound interest is not the amount, it is time.

Now the flip side. Compound interest works on costs too. One percent a year sounds like little. Do the math: the same 10,000 euros, 40 years, seven percent. Without costs you end up with almost 150,000 euros. With one percent in costs a year, about 103,000 are left. Almost 47,000 euros less, almost a third of your result. Not because the market was worse, but because every year a small part is missing, and that part earns nothing anymore either.

How expensive is a fund today? We counted in our ETF directory. Of 556 ETFs with a cost figure, the cheapest costs 0.02 percent a year, the middle value is 0.30 percent, and more than one in three costs 0.20 percent or less. An active fund from a bank, on the other hand, is often around 1.5 percent. The difference sounds small. Let's see what it does to a savings plan.

200 euros a month, for 30 years. In total you paid in 72,000 euros. At seven percent a year and 0.30 percent in costs, that becomes just over 221,000 euros. With 1.5 percent in costs, it is about 178,000. That is more than 43,000 euros of difference, more than half of everything you paid in. And all of it in exactly the same market.

The same works in the other direction. Two percent more return a year, so nine instead of seven, turns 10,000 euros over 30 years not into 76,000 but into almost 133,000. Five percent more, so twelve, would be almost 300,000, four times as much. Sounds tempting. But honestly: beating the market by five percent every year for decades is something almost nobody manages. Most active funds even trail the market after costs, as you saw in the lesson on research. If someone promises they will surely do it, don't trust them.

And the last example, maybe the most important one. If a stock loses 50 percent and then rises by 50 percent, you are not back to zero. You have still lost a quarter. To make up a 50 percent loss, you need a 100 percent gain. At minus 20, plus 25 is enough; at minus one third, you need plus 50. So big losses cost far more time than they seem at first glance. That is why it pays to check before you buy whether the price fits what the company really delivers.

To sum up. First: with compound interest, time matters more than the amount. Second: costs grow just the same, one percent can cost a third. Third: extra return has a huge effect, but it is rare, so distrust promises. Fourth: big losses need even bigger gains.

In the Fair Value Calculator, the ETF directory shows you the running costs of every fund, and for more than 35,000 stocks whether the price is above or below the value the numbers support. Important: this is not financial advice.