What Is Compound Interest?

The formula behind compound interest

Compound interest is calculated with A = P(1 + r/n)^(nt), where P is the principal (your starting amount), r is the annual interest rate as a decimal, n is how many times per year interest compounds, and t is the number of years. A is the ending balance.

Simple interest, by contrast, only ever applies to the original principal: interest = P × r × t. Put $10,000 into an account paying 7% a year, and simple interest hands you a flat $700 every single year, no matter how long you leave it there. Compound interest, calculated annually on the same $10,000 at 7%, hands you $700 in year one too, but by year two the 7% is applied to $10,700, not $10,000. The gap between the two methods barely shows in year one. By year thirty, simple interest has grown that $10,000 into $31,000. Compound interest has grown it into $76,123, more than double, from the exact same rate and the exact same money.

Why compounding frequency matters

The n in the formula, how often interest is added to the balance, matters less than most people assume, but it isn't nothing. Compare $10,000 at 6% for 10 years: compounded once a year, it grows to about $17,908. Compounded monthly, the same rate and the same decade produces about $18,194. Roughly $286 of difference, from changing nothing but how often the interest gets calculated.

A faster way to estimate how long money takes to double, without running the full formula, is the Rule of 72: divide 72 by the interest rate. At 7%, that's roughly 10.3 years. At 4%, it's 18 years. It's an approximation, not an exact answer, but it's close enough for a gut check.

In practice, most savings accounts and investment platforms compound daily or monthly, and most credit cards do too. The exact frequency rarely changes the outcome as much as two other factors: the rate itself, and how long the money sits there. Plug your own numbers into our compound interest calculator to see the effect on your own balance.

Time is the real multiplier

Rate gets most of the attention, but time does more of the actual work, mostly because people underestimate how non-linear compounding is. Someone who invests $200 a month at a 7% annual return starting at age 25 and stopping at 65 ends up with roughly $525,000 by retirement. Someone who starts the identical $200-a-month habit at 35 instead, and also stops at 65, ends up with roughly $244,000.

That's a 10-year head start turning into more than double the final balance, despite the second saver contributing only $24,000 less in total ($200 a month over 10 fewer years). Almost the entire $281,000 gap comes from those first 10 years of growth being left alone to compound for the following 30, not from any extra money going in.

This is the actual argument for starting young, and it has nothing to do with willpower or discipline. A dollar invested at 25 has more years left to double, and double again, than a dollar invested at 35, regardless of how good either person is at saving. If retirement math like this interests you, our guide to FIRE builds directly on it.

Compound interest can work against you too

Nothing about the math cares which direction it's applied. A credit card balance compounds the same way a retirement account does, just working against the person carrying it instead of for them. Carry a balance at a typical credit card APR in the low-to-mid twenties, and the interest that accrues gets added to what you owe, so next month's interest is calculated on a bigger number than this month's.

This is why paying only the minimum on a high-interest balance can stretch a debt out for years and quietly double or triple what was actually borrowed. It's the same formula from the earlier sections. The sign is just flipped.

Mistakes that quietly cost the most

Waiting a few years to start is the most expensive mistake, precisely because of what the previous section showed: the earliest years of compounding matter more than any later ones, and they can't be recovered once the time has passed.

Chasing a higher rate without weighing the added risk is a close second. A higher expected return that comes with wide swings can wipe out years of contributions in a single bad stretch, and recovering from a loss requires a larger percentage gain than the loss itself.

Ignoring fees is the quiet one. An account with a 1.5% annual expense ratio versus one with a 0.1% ratio doesn't look like much of a difference year to year, but that gap compounds too, working exactly like the interest above, just subtracting instead of adding.

So does inflation. A 7% return sounds solid until 3% inflation is subtracted from it, leaving a real return closer to 4%. Compound interest is still working, just against a number that's smaller than the one advertised.