This is the money in your bank account and the money on a loan. No formula until you have already worked it out by hand.
one sentence
Money you earn as interest starts earning interest of its own. So next year you earn interest on a bigger pile than you had this year — and the pile keeps getting bigger.
That is the only difference from simple interest. With simple interest you always earn on the original amount. With compound interest you earn on everything you have, including what you earned last time.
Start with what interest is. You put €1,000 in a bank. The bank uses your money, so it pays you for the use of it. If it pays 10% a year, that means for every €100 you leave there, it gives you €10 at the end of the year. On €1,000 that is €100.
Now the question that matters. At the start of year two, how much money is in the account? €1,100 — your original €1,000 plus the €100 you were paid.
So in year two, is the bank paying you 10% of €1,000, or 10% of €1,100?
That single question is the whole topic. If the answer is €1,000, it is simple interest — you always earn on the original amount and nothing else. If the answer is €1,100, it is compound interest — you earn on whatever is actually sitting there.
Real savings accounts, fixed deposits, loans and credit cards almost all use the second one. So the €100 you earned in year one starts earning money for you in year two. It is working, the same as your original €1,000 is working.
And it works exactly the same against you. On a loan or a credit card, unpaid interest gets added to what you owe, and then you are charged interest on that too. This is why an unpaid card balance grows so much faster than people expect. The mathematics does not care which direction it is pointing.
What is different about compound interest?
The interest itself earns interest.
So the amount it is worked out on grows every year.
First work through this part
The questions open once you have been through the explanation. Take your time — nothing here is a race.
First get the quick-check questions in the section above right — then this one opens.
First get the quick-check questions in the section above right — then this one opens.
First get the quick-check questions in the section above right — then this one opens.
Work through the sections above first — then the revision cards open.
First get every section's quick-check right above — then the practice, guided and test questions open.
First work through every section above — then the final test opens.