Money is like magic for most people. For example, you put $1,000 into your savings account, and forget about it. When you remember to check up on it, you see that it's grown. Maybe it grew by a little, or maybe it grew by a lot, but the point is that money just showed up out of nowhere. Money you did nothing to earn, and which has increased your personal wealth by a little bit.
It's not magic, though, it's interest.
Interest is officially defined as the cost paid for borrowing someone else's money. So, if you take out a loan, that loan comes with interest (which means that, while you borrowed $1,500 initially, you may be paying back $2,000 when all is said and done). If you leave your money in the bank, then the bank pays you for the privilege of hanging onto it.
How It Works
Let's start with simple interest. Simple interest is calculated off of the principal (the amount of money you started with), and it never changes. So, let's say you borrow $500 from your roommate, and the two of you agree to a rate of 1%. That means every time you make a payment, there's going to be a $5 fee taken out. If it takes you 10 months to pay back, then your roommate earned $50 off of this loan.
With simple interest, it doesn't matter how much of the initial balance you've paid off; the interest on every payment is always the same.
How It's Different
Compound interest is like simple interest's more interesting cousin. They're related, but very, very different.
Let's use a different example here. Say you open a savings account, and you toss in $1,000. The bank gives you a 1% interest rate, compounded monthly. Now, if this was simple interest, you'd get $10 every time, no matter what. Because it's compound interest, though, you earn more.
Every time you earn with compound interest, the amount you earn is added to the principal balance. Even if it's only a few dollars, it is still counted when your next interest payment is taken into account. If you leave the account alone, then it will grow as more, and bigger, payments are added.
There's even a formula for figuring out how much money you're going to earn. The formula is:
P = C (1 + R/N) NT
In this equation P is the future value of your account. C is the initial deposit value. R is the interest rate, N is the number of times per year your interest is compounded, and T is the number of years on your investment. If you plug in the numbers, figuring out how much money you're going to make is actually pretty simple!
More Useful Finance Explanations
If you've got other questions about how the financial world works, then you might find these topics of interest.