How Compound Interest Actually Works, With Real Numbers

Say you put $10,000 into something that grows 7% a year and you never touch it. After year one you have $10,700. In year two you earn 7% of $10,700, not of the original $10,000, so the gain is $749 instead of $700. That extra $49 is interest earned on interest, and it is the whole mechanism.

Compare that with simple interest, where you only ever earn 7% of the original $10,000, which is $700 a year. After 10 years simple interest leaves you with $17,000 and compounding leaves you with $19,671.51. After 20 years it is $24,000 against $38,696.84. After 30 years it is $31,000 against $76,122.55. You can check any of these in the compound interest calculator. The figures here assume the interest is added once a year.

Look at the 10-year numbers again. Compounding is ahead by $2,671.51, which is real money but hardly life-changing, and it's easy to decide the whole idea is overhyped. Then look at year 30, where the compounded balance is more than double the simple one. The curve is shallow for a long time and then it isn't. Most of the growth in a 30-year balance happens in the last ten years, because that is when the balance being multiplied is large.

It also explains why a few points of return matter more than they sound. The same $10,000 over 30 years becomes $32,433.98 at 4%, $76,122.55 at 7% and $174,494.02 at 10%. Three percentage points in either direction changes the end result by tens of thousands of dollars.

There's a quick way to estimate this without a calculator. Divide 72 by the annual return and you get the number of years it takes money to double. At 7%, 72 ÷ 7 is about 10.3 years. The exact figure is 10.24 years, so the shortcut is close. It drifts when rates are very high or very low, and it works best somewhere between about 6% and 10%.

It runs backwards too. If you need money to double in 6 years, you need roughly 12% a year, and that tells you something about how realistic the goal is.

The example that tends to change minds uses monthly saving instead of a lump sum. Put $200 a month into the same 7% account. After 10 years you'd have about $34,617. After 20 years, $104,185. After 30 years, $243,994, of which you contributed $72,000 yourself. The other $171,994 is growth.

Now picture two people. One saves $200 a month for 30 years. The other waits ten years and then saves the same $200 for 20 years. The second person pays in $24,000 less and finishes with $139,809 less. A ten-year head start outweighs almost anything you could do later by picking a slightly better investment. You can try your own numbers in the savings goal calculator, or run a full projection with the retirement calculator.

Compounding doesn't care which side of the transaction you're on. A credit card balance charged around 20% or more compounds the same way, which is why minimum payments barely move the balance. To see how long a card balance really lasts, the credit card interest calculator will show you.

Everything above assumes a steady, guaranteed return, and nothing is steady or guaranteed. Real investments rise and fall, and a bad stretch early on can matter a great deal. The figures also ignore fees, taxes and inflation, all of which reduce what the money can actually buy. Treat the examples as a way to understand how the mechanism behaves, not as a forecast of what your own account will do.