How compound interest works
Covers What Is Interest?, Simple vs. Compound Interest, The Compound Interest Formula and more.
“How compound interest works” is a 4-lesson course at Teen level, created with soclever, a personal AI teacher. Each lesson takes a few minutes and ends with a check-in question; finish the curriculum and you can take a certificate test to earn a diploma. Try the first lesson without an account — or make your own course on any topic.
What you'll learn
- What Is Interest?. A lot of people think interest is just something banks do to make extra money off you—like a hidden fee. That's backwards.
- Simple vs. Compound Interest. Think of a small apple tree. Each year it gives you ten apples, always ten, no matter what.
- The Compound Interest Formula. Think of a snowball rolling downhill: as it rolls, it picks up snow, and the bigger it gets, the more snow it picks up each turn.
- Exponential Growth and Euler's Number. Think of a snowball rolling downhill: the bigger it gets, the more snow it picks up, so it grows faster and faster. Compound interest works the same way.
Lesson 1: What Is Interest?
A lot of people think interest is just something banks do to make extra money off you—like a hidden fee. That's backwards. Interest is the price of using someone else's money, and it flows in both directions depending on which side of the deal you're on.
When you borrow money—say, a loan for a car—you pay interest to the lender. You're renting their money, and interest is what that rental costs. When you deposit money in a savings account, the bank borrows from you, and they pay you interest as a reward for letting them use your cash. Same mechanism, opposite direction.
Here's a real example. You put $1,000 in a savings account that earns 5% interest per year. That 5% is the annual rate—the percentage of your money that the bank will give back to you as a reward. After one year, you earn $50 (that's 5% of $1,000). You now have $1,050. The bank needed your money to lend out to other customers, so they paid you for the privilege.
Interest is always a percentage of the amount borrowed or saved. The bigger the balance or loan, the more interest accrues. The higher the rate, the faster your money grows—or the more you owe.
Questions this course answers
What is interest?
Interest is the price of using someone else's money, and it flows in both directions depending on which side of the deal you're on.
How does simple interest work?
With simple interest, you earn money only on the amount you first put in.
What does P represent in the compound interest formula?
P is the principal, the amount you start with.
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