Lesson 1.2 · 2 of 5 · First steps
Compound interest explained simply, with a calculator and exercises
Compound interest means earning returns on your earlier returns, not only on the money you started with. The longer you leave it, the faster it grows: at 7% a year, money doubles in about 10 years.
Terms in this lesson
- Compound interest
- You earn on your past earnings too, not just on the amount you started with.
- Total return
- The gain from the price plus the dividends, compared with what you paid.
- Inflation
- How much prices rose in a year: how much buying power your money lost.
Opening question
You put $1,000 away at 10% a year and take nothing out. How much do you have after 2 years?
In year one you earn $100. In year two you earn 10% of $1,100, which is $110. Total: $1,210. The extra $10 is interest on interest.
It does not matter if you get it wrong: trying first helps you remember.
What compound interest is
Definition
What is compound interest?
Returns on your returns.
With compound interest, each year’s gain is added to your money, and the next year you earn on that gain too. The total grows faster and faster, like a snowball picking up more snow as it rolls.
$1,000 at 10% a year, nothing withdrawn.
Work it out
You have $2,000 at 5% a year, compounded. How many dollars do you have after 2 years?
A hint
Multiply by 1.05 twice.
$2,000 × 1.05 = $2,100 after year one; $2,100 × 1.05 = $2,205 after year two.
Compound interest versus simple interest
Example
How much difference over 30 years?
Almost 2.5 times as much.
$10,000 at 7% a year. With simple interest you always earn $700 a year, on the starting amount only. With compound interest you also earn on your gains, and the gap widens every year.
After 30 years, before tax and fees.
Myth or fact?
“Compound interest only works with savings accounts.”
Myth. It works wherever your gains stay invested: savings, bonds, shares with reinvested dividends, or an accumulating ETF that reinvests dividends for you.
Work out what you can build by investing monthly
Most people do not invest one lump sum. They put in a little every month. Move the sliders to see how much of the total you paid in and how much is growth.
Why it matters when you start investing
Example
Anna and Ben each invest $200 a month
Anna invests for 10 years, Ben for 30. At 65, Anna has more.
Anna starts at 25 and stops at 35, paying in $24,000. Ben starts at 35 and keeps going until 65, paying in $72,000. At 7% a year, Anna’s money has ten extra years to compound.
Values at 65, 7% a year, compounded monthly, before tax and fees.
Estimate
At 7% a year, how many years does it take for money to double? Give a range you think contains the answer.
This exercise is in the free account, where we also save your progress.
Create a free accountCheck yourself
What matters most for compound interest?
This exercise is in the free account, where we also save your progress.
Create a free accountWhat would you do?
You can set aside $300 a month. What do you do?
This exercise is in the free account, where we also save your progress.
Create a free accountWhat you learned
- Compound interest means earning returns on your earlier returns.
- Time matters more than the amount: starting early is a big advantage.
- The rule of 72: divide 72 by the return to estimate how many years it takes to double.
You reached the end
Keep what you learned
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Save your progress with a free accountLessons are educational. They are not a recommendation to buy or sell. Investing involves risk and you can lose money. Sources: calculations assume constant returns, before tax and fees; long-run real returns on global shares: UBS Global Investment Returns Yearbook.