Compound interest
With compound interest your earnings earn more earnings. For a long time not much seems to happen, and the effect only gets really big in the later years. That's why starting early does more than paying in a lot.
Learning objective: After this lesson you can calculate compound interest and explain why starting early does more than paying in a lot.
With simple interest you get the same amount every year. With compound interest last year's interest earns interest too. So each year you get interest on a slightly bigger amount.
Start versus end
At first the difference is tiny, at the end it's huge. At 7 percent a year €10,000 turns into about €19,700 after ten years. After twenty years it's about €38,700, almost twice as much. After thirty years about €76,100.
Time beats amount
That has a consequence many people don't like. Time matters most, and how cleverly you invest matters less. Lea and Ben each invest €200 a month, assuming 7 percent a year. Lea starts at 25, Ben at 35, and both stop at 65. Lea pays in €96,000, Ben €72,000. In the end Lea has about €525,000 and Ben about €244,000. Costs and taxes aren't taken off, but that changes the ratio very little.
The rule of 72
For mental arithmetic there's the rule of 72. Divide 72 by the return in percent and you get roughly the years until your money doubles. At 6 percent that's twelve years, at 9 percent eight.
A sum invested once grows by a factor of (1 + interest) every year. After n years you have the starting amount times (1 + interest) to the power of n. If you add money regularly, many small amounts that grow for different lengths of time add up. Either way the number of years sits in the exponent. That's why the gain is biggest in the last years: each year's interest lands on an amount that has already grown.
Where the 72 comes from
The rule of 72 is a shortcut. The exact value is the natural logarithm of 2 divided by the logarithm of (1 + interest), which comes out closer to 69 or 70. People still use 72 because it divides nicely and is actually a bit more accurate between 6 and 10 percent.
Compounding applies to costs
The same mechanism works on costs. Over thirty years, one percentage point less return takes about a quarter off the end amount. If Lea gets 6 instead of 7 percent because her fund costs one percent a year in fees, she ends up missing roughly one euro in four. Small costs look harmless and over a long time they aren't.
Summary
- Compound interest works late, but then it's strong.
- 72 divided by the return gives the years until your money doubles.
- Costs grow over the years just like earnings do.
Did you get it?
How long does it take to double at 8 percent?
About nine years, because 72 divided by 8 is 9.
Why is the gain biggest in the last years?
Because each year's interest lands on an amount that has already grown.
Why do fees have such a strong effect over a long time?
Because they grow through compounding just like earnings, only at your expense.
Check your understanding
Your task
Take $5,000 at 6 percent per year over 15 years and check your result in the compound interest calculator. Use the rule of 72 to find roughly after how many years the money doubles. Then enter your own numbers and note what starting one year earlier makes.