How compound interest actually works
Simple interest pays you only on the money you originally deposited. Compound interest pays you on your deposit *and* on the interest that deposit has already earned. That second part is what makes the curve bend upward instead of running in a straight line.
In the first few years the difference looks trivial — a few hundred dollars. The gap widens slowly, then suddenly. With a 7% return, money roughly doubles every ten years, so the final decade of a thirty-year run adds more absolute dollars than the first two decades combined. This is why starting early beats contributing more later, and it is the single most important idea in personal finance.
The formula
For a lump sum with no ongoing contributions, the standard formula is A = P(1 + r/n)^(nt), where P is your principal, r is the annual rate as a decimal, n is how many times per year interest compounds, and t is the number of years.
Once you add regular monthly contributions the closed form gets messier, so this calculator simulates month by month instead. It converts your nominal rate at the chosen compounding frequency into an equivalent monthly rate, applies it to the running balance, then adds your contribution at the end of each month. That ordering matters: a contribution made at the end of a month earns nothing during that month, which is the conservative and more common assumption.
A worked example
Start with $10,000, add $500 a month, and assume a 7% annual return compounded monthly. After 20 years the balance is roughly $301,000. Of that, $130,000 is money you deposited yourself and about $171,000 is interest.
Now change one thing: extend to 30 years instead of 20. The balance grows to roughly $691,000 — more than double, from adding 50% more time. Your own contributions only rose to $190,000. Every extra dollar came from compounding on money that was already there.
Compounding frequency matters less than you think
People often obsess over whether an account compounds daily or annually. At a 7% nominal rate, annual compounding yields exactly 7% and daily compounding yields about 7.25% effective. Over twenty years that gap is real but small — worth maybe 4% of your final balance.
Your contribution rate and your time horizon each move the outcome by several hundred percent. Frequency moves it by a few percent. Optimise the big levers first.
What this calculator does not account for
Three things will make your real-world result lower than the number above. Inflation erodes purchasing power at roughly 2–3% a year, so a 7% nominal return is closer to 4–5% in real terms. Taxes on interest, dividends, and capital gains apply outside of tax-advantaged accounts. And investment fees — an expense ratio of 1% instead of 0.05% can consume a fifth of your final balance over thirty years.
Also worth remembering: a fixed 7% return is a modelling convenience, not a promise. Real markets deliver that as a long-run average made of violent up and down years. Sequence of returns matters a great deal if you are drawing the money down rather than accumulating it.
Frequently asked questions
- What interest rate should I use?
- For a savings account or CD, use the rate your bank quotes. For a diversified stock portfolio, 7% is a common long-run assumption for US equities after inflation-adjusted historical averages; 10% is the rough nominal historical figure. Being conservative costs you nothing.
- Does this account for inflation?
- No. The result is in nominal dollars. To estimate purchasing power in today's money, subtract roughly 2–3% from your rate before calculating.
- What is the difference between APR and APY?
- APR is the nominal annual rate before compounding. APY (or effective annual rate) includes the effect of compounding, so it is always equal to or higher than APR. The calculator shows the effective rate so you can compare accounts fairly.
- Does it matter if I contribute at the start or end of the month?
- Slightly. Contributing at the start gives each deposit one extra month of growth. Over 20 years that is worth roughly half a percent of your final balance. This calculator assumes end-of-month, the more conservative choice.