What this calculates
Enter a starting amount, a rate and a term, and this shows what the money grows into, how much of the final balance is your own and how much is interest. Add a regular deposit and it accounts for those too, each one earning from the period it lands in.
The figure worth watching is not the final balance but the split beneath it. Over a long enough term the interest overtakes everything you paid in, and the year-by-year table shows exactly when that happens.
The formula
For a single lump sum, the whole thing is one expression. P is the amount you start
with, r the annual rate as a decimal, n the number of compounding periods in a
year, and t the number of years.
Final balance
A = P × (1 + r ÷ n)^(n × t)The rate for one period
Period rate = r ÷ nWhat the money earned
Interest = A − PRegular deposits are not part of that expression — each one compounds only for the time left after it arrives, so a deposit made in the final year earns almost nothing. Where the deposit and compounding schedules line up, the series has a closed form.
Future value of the deposits
FV = C × ((1 + i)^m − 1) ÷ iThis calculator steps through the periods instead of using that formula, because the two schedules often do not line up — monthly deposits into a quarterly-compounded account are ordinary — and stepping handles any pairing. A deposit lands at the end of the period it falls due in, which is what a bank actually does: money paid in during a period earns nothing until that period closes.
Worked example
Look at how the yearly interest changes rather than just the total. The first year earns 8,000. The tenth earns 15,992 — almost double, on exactly the same rate, because it is being paid on a balance that has itself been growing. Nothing was added along the way; the acceleration is the whole point.
Now change only the schedule. The same 100,000, the same 8%, the same ten years:
- compounded annually — 215,892.50
- compounded half-yearly — 219,112.31
- compounded quarterly — 220,803.97
- compounded monthly — 221,964.02
- compounded daily — 222,534.58
The gap between the best and worst of those is 6,642.08, and most of it is won in the first step from annual to half-yearly.
When to use it, and the mistakes to avoid
Use it when comparing deposit or investment options, when deciding how long to leave money alone, when working out what a regular monthly amount turns into, and when a product quotes a rate without saying how often it compounds.
The mistakes that cost the most:
- Reading the rate without the schedule. "8%" is not one number. Ask how often it compounds before comparing two products, and compare the final balance rather than the headline rate.
- Chasing compounding frequency. It is real but small. Above, daily beats monthly by about 571 over a decade, while one extra percentage point of rate is worth many times that.
- Assuming deposits earn from day one. A deposit starts earning at the end of the period it lands in, and one made near the end of the term barely compounds at all. Starting earlier beats paying in more later.
- Being surprised that the interest exceeds the principal. Over a long enough term that is normal, not an error — at 8% for ten years the interest is already larger than the amount invested.
- Treating the final balance as spendable. It is a nominal figure, before tax on the interest and before inflation. Neither is applied here.
- Comparing a lump sum with a deposit plan on the final balance alone. Check what went in as well; a larger balance built from far more of your own money is not necessarily the better outcome.
FAQ
How is compound interest calculated?
Each period the balance earns interest, that interest is added to the balance, and the next period's interest is worked out on the larger figure. For a lump sum it collapses to A = P(1 + r/n)^(nt), where r is the annual rate as a decimal, n is how many times a year it compounds and t is the number of years. The compounding is what separates it from simple interest, which only ever pays on the original amount.
What is the difference between monthly and annual compounding?
How often the interest starts earning on itself. Take 100,000 at 8% for ten years: compounded once a year it reaches 215,892.50, and compounded monthly it reaches 221,964.02. Same rate, same money, same term — about 6,072 apart purely from the schedule. The more often it compounds, the sooner each slice of interest begins earning.
Does more frequent compounding always earn more?
Yes, but with sharply diminishing returns, and the quoted rate matters far more than the schedule. On that same 100,000 at 8% for ten years, going from annual to half-yearly adds about 3,220; going from monthly all the way to daily adds only about 571. Going from 8% to 9% would add far more than any change of frequency.
How much will 100,000 grow to?
At 8% compounded annually it is 215,892.50 after ten years, of which 115,892.50 is interest — more than the amount you started with. Change the rate, the term or the compounding above and the figure updates as you type. Adding a regular deposit changes it far more than tweaking the rate does.
How long does money take to double?
Divide 72 by the rate for a close estimate: at 8% that suggests nine years. It holds up here — 100,000 at 8% compounded annually reaches 199,900.46 after nine years, a hair under double, and passes it early in the tenth. The rule is an approximation, but a good enough one to do in your head.
Does this account for tax or inflation?
No. It shows the nominal balance: what the account statement will say, not what it will buy. Interest is usually taxable, and inflation erodes the real value of the final figure, so treat the result as the gross outcome before both. Neither is applied here because both depend on your country and your bracket.