What compound interest is
Compound interest is the interest your money earns on the interest it already earned. In the first period you earn on what you put in; in the second, you earn on what you put in plus what you've already made. That small detail is what separates an account growing in a straight line from one that takes off after a few years.
It's also why starting early matters more than starting big: time does most of the work.
The formula
For a starting amount with no contributions, the future value is:
- FV — future value (what you'll have at the end)
- P — starting amount
- r — annual rate as a decimal (7% becomes 0.07)
- n — how many times a year it compounds (12 if monthly)
- t — years
If you also contribute every month, those deposits form an annuity: each one arrives at a different moment and grows for whatever time it has left. The calculator above solves both parts and adds them together.
Why compounding frequency changes the result
Compounding means turning earned interest into capital. The more often it happens, the sooner that interest starts generating more interest. With the same annual rate, compounding monthly gives slightly more than compounding yearly. The gap is tiny over one year and noticeable over twenty.
The rule of 72: divide 72 by your annual return and you get roughly how many years it takes your money to double. An 8% return? 72 ÷ 8 = 9 years. It's a surprisingly good mental shortcut.
Compound vs. simple interest
With simple interest only the original amount earns a return: the interest is taken out and never goes back to work. That's the dashed line in the chart above. Early on the two lines almost overlap; somewhere around year seven or eight they separate and never meet again.
How to read your result
Look at two numbers more than the total: what you contributed and the interest earned. When the interest overtakes your contributions, your money is working harder than you are. That crossover usually arrives sooner than people expect, and it is the moment when leaving the investment alone really pays.
One honest caveat: these numbers assume a constant return, and reality is not constant. Markets go up and down. Treat the result as a sense of scale, not a promise.