Understanding compound interest
Updated
What compound interest is
Compound interest is interest that earns interest too. In the first month, your money earns on what you put in. In the second, it earns on what you put in plus what it already earned. And so on.
Picture a snowball rolling down a hill. At first it’s small and barely grows. But every turn picks up more snow than the one before, because the ball is bigger. Near the bottom, it grows more in a single turn than it did on the whole way down.
The math behind it
For a single amount saved once, the formula is:
A = P × (1 + r)n
A is the final amount, P is what you put in, r is the rate per period and n is the number of periods. The secret lives in n, sitting up there as an exponent. That’s why time matters more than the rate. When you add money every month the formula gets longer, and that’s exactly what the calculator does for you.
An example with real numbers
Say you save $300 a month for 20 years, earning 7% a year. You put in $72,000 yourself. At the end, you have about $152,000. Around $80,000 came from interest, not from you.
Now notice the part most people miss: halfway there, after 10 years, the balance is only about $51,000. Most of the growth happens in the second half. The snowball only shows its size near the bottom of the hill.
How long it takes to double your money
There’s a shortcut you can do in your head, the rule of 72. Divide 72 by the yearly rate and you get roughly how many years it takes to double. At 7% a year, about 10 years. At 9%, about 8.
What the math doesn’t show
If the math is so generous, why don’t more people start? Because the brain likes rewards now. Saving $300 hurts today, and the prize only shows up years later. In the first months the growth looks so small that quitting is tempting, right when the snowball is still at the top of the hill.
Once you understand that, you stop checking your balance every day waiting for a miracle. We talk more about this tug of war between now and later in the quick reward trap.
Frequently asked questions
What’s the difference between simple and compound interest? With simple interest, earnings are always based on the starting amount. With compound interest, they’re based on the amount that has already grown. Over a short time the gap is small; over 20 years it’s huge.
Monthly or yearly rate? The calculator accepts both. Just don’t divide the yearly rate by 12, because that gives a slightly higher number than the real one. Let the calculator convert it.
Does it include taxes and inflation? No. It shows gross growth. For a more realistic picture, use a rate a little lower than advertised.
Is it worth starting small? Yes, because time is what matters most. Someone who starts with $100 today usually ends up ahead of someone who waits five years to start with $500.
Next step: want to know how much to save to reach a specific amount? Try the first million calculator.
