What is compound interest?
Compound interest is when you earn interest on the money you saved and on the interest you already earned. Simple interest pays only on the original amount. The difference looks tiny at first and large later.
Hypothetical: $1,000 at 5% a year earns $50 in year one, for $1,050. In year two the 5% applies to $1,050, so it earns $52.50 and the balance reaches $1,102.50. Over 30 years at 6%, simple interest turns $1,000 into $2,800; compounding once a year turns it into about $5,743. That widening gap is what the drawing at the top shows.
The same math works against you on debt: unpaid card interest is added to the balance and then charges interest itself. Reinvested dividends work in your favour the same way, as the dividend investing guide explains.
The compound interest formula, explained
For a single amount, the compound interest formula is A = P(1 + r/n)^(nt), with each letter defined in the list below.
Monthly vs yearly compounding, hypothetical: $10,000 at 6% for 10 years becomes $17,908.48 compounded yearly and $18,193.97 compounded monthly, about $285 more. Monthly compounding at 6% works out to about 6.17% a year, which is why US deposit accounts disclose an annual percentage yield (APY) that already includes compounding. The frequency matters far less than the rate and the number of years.
- A = the final amount.
- P = the starting amount (principal).
- r = the annual rate as a decimal: 6% = 0.06.
- n = how many times a year interest is compounded: 12 for monthly, 1 for yearly.
- t = the number of years.
How monthly contributions add to compound growth
Regular contributions compound too. With a contribution at the end of each month and monthly compounding, the formula gains a second term: A = P(1 + i)^N + PMT × ((1 + i)^N − 1) ÷ i, where i = r ÷ 12 is the monthly rate, N = 12 × years is the number of months and PMT is the monthly contribution.
Hypothetical: $5,000 to start, $200 a month, 6% a year compounded monthly, for 30 years. You put in $77,000 in total and the balance reaches about $231,016, so about $154,016 came from growth. In year one, growth adds only $375.50; by year 20, total growth has passed everything you contributed. The drawing shows the same pattern.
How to use the compound interest calculator
The calculator above runs these steps in your browser and stores nothing you type. Using the example from the previous section:
- Starting amount: what you invest today, for example $5,000. Enter 0 if you start from nothing.
- Monthly contribution: what you add each month, for example $200. The calculator adds it at the end of each month.
- Annual return (%): the yearly return you assume, for example 6. Try a lower rate too, because this is a guess, not a forecast.
- Years: from 1 to 50, for example 30.
- Compounding: monthly or yearly. Monthly ends slightly higher at the same rate.
- Read the results: Final balance (about $231,016 here), Total contributed ($77,000, the start plus every monthly contribution) and Total growth (about $154,016). The year-by-year table lists Year, Contributed, Growth and Balance, so you can see when growth overtakes what you put in.
Starting early vs starting late: a worked example
Time is the strongest input. Two hypothetical investors each put in $96,000 at an assumed 6% a year, compounded monthly. Investor A adds $200 a month for 40 years and ends with about $398,298. Investor B adds $400 a month for only the last 20 of those years and ends with about $184,816. Same money in, yet A ends with more than twice as much, because A’s early contributions compounded for twice as long.
Now the downside. If A’s return averages 3% instead of 6%, the same 40 years end at about $185,212, less than half the first estimate. And a 30% market fall in the final year would cut $398,298 to about $278,809, however long it took to build. The calculator assumes the same return every year; real markets never deliver it that way, as the bull vs bear market guide shows.
Fees and inflation: what the result does not subtract
The calculator shows growth before costs. A yearly fee is taken from the whole balance, so you also lose the return that money would have earned. To see the effect, lower the return by the fee: the same $5,000 plus $200 a month at 5% instead of 6%, as a rough model of a 1% yearly fee, ends near $188,790 instead of $231,016. That is about $42,225 less, more than half of the $77,000 you put in. Compare fund costs in ETF vs mutual fund.
Inflation is the other leak. Prices tend to rise, so a dollar buys less later; in the US, the Bureau of Labor Statistics tracks this with the Consumer Price Index (CPI). If inflation averages a hypothetical 3% a year, divide the result by 1.03 to the power of the years: $231,016 in 30 years buys about what $95,175 buys today. Taxes, which depend on your country and account, are not included either.
Why the assumed return is not a promise
The number you type in Annual return (%) is an assumption. Real returns change every year and can be negative, stocks can lose a large part of their value for years, and past averages do not predict the next decade. The smooth curve a calculator draws is a planning sketch, not a forecast.
Monthly contributions behave differently in a real, bumpy market. Hypothetically, $200 buys 4 shares at $50, 5 at $40 and 8 at $25: the same dollars buy more shares when prices are low, so your average cost ends below the average price, as in the drawing. That is dollar-cost averaging. It does not prevent losses: if prices keep falling, every contribution loses value too.
Practical habits: run the calculator at two or three returns, including a low one; keep money you need soon out of investments that can fall; treat the result as a range, not a number. The how to invest in stocks guide covers the first steps. This is education, not advice; consider your own situation.