How to use the compound interest calculator
- Enter the Initial amount you are starting with (it can be 0).
- Enter a Regular contribution and choose per month or per year. Then choose whether contributions are paid at the End of each period (the usual assumption, for example a deposit on payday at the end of the month) or the Start of each period.
- Enter the Annual interest rate and pick the Compounding frequency: yearly, half-yearly, quarterly, monthly, daily or continuously.
- Set the term in Years and Months.
- Optionally open Contribution increase, inflation and currency to raise your contributions by a percentage each year, add an inflation rate to see the value in today's money, or change the currency symbol.
- Read the final balance, total contributions, total interest and the effective annual rate. The chart and the Year-by-year table show how the balance builds up, and How your result was calculated works through the formula with your numbers.
The compound interest formula
Compound interest means you earn interest on earlier interest as well as on the money you put in. For a single sum the formula is A = P(1 + r/n)nt, where P is the starting amount, r the annual rate as a decimal (5% = 0.05), n the number of times interest is added each year and t the number of years. With continuous compounding it becomes A = Pert.
Regular deposits are added with the future value of a series (an annuity): FV = PMT × ((1 + i)N − 1) / i, where PMT is each deposit, i the interest rate per deposit period and N the number of deposits. If you pay at the start of each period, every deposit earns one more period of interest, so the result is multiplied by (1 + i). The final balance is the two parts added together.
When deposits and compounding don't line up
Accounts often compound at a different frequency from your deposits. This calculator uses the standard equivalent periodic rate method: it converts the rate into the rate per deposit period that gives exactly the same growth over a year, i = (1 + r/n)n/m − 1, where m is the number of deposits a year. For 5% compounded yearly with monthly deposits, that is 1.051/12 − 1 ≈ 0.4074% a month. Each deposit then grows at that rate until the end, and the starting amount still grows by exactly (1 + r/n)nt.
Some banks instead pay simple interest on deposits made part-way through a compounding period, which gives a very slightly different figure. With a yearly increase in contributions, each deposit is grown to the end separately and added up; the table and the result still agree to the cent.
Effective annual rate (APY or AER)
The more often interest compounds, the more a given nominal rate is really worth. The effective annual rate, called APY (annual percentage yield) in the US and AER (annual equivalent rate) in the UK, folds compounding into one yearly figure: (1 + r/n)n − 1. A 5% rate compounded monthly is worth 5.116% a year, compounded daily 5.127%. Use it to compare savings accounts that compound differently.
| 1,000 at 5% for 10 years, compounded | Final balance | Effective annual rate |
|---|---|---|
| Yearly | 1,628.89 | 5.000% |
| Quarterly | 1,643.62 | 5.095% |
| Monthly | 1,647.01 | 5.116% |
| Daily (365) | 1,648.66 | 5.127% |
| Continuously | 1,648.72 | 5.127% |
Frequency matters much less than the rate and the time: yearly to daily compounding adds under 20 here.
Inflation and real value
If you enter an inflation rate, the calculator divides each balance by (1 + inflation)t to show its real value, meaning what it could buy in today's prices. A balance that grows at 5% a year while prices rise 3% a year gains only about 2% a year in buying power. Tax on interest, account fees and fund charges also reduce real growth; this calculator does not deduct them, so enter a rate after fees if you know it.
For a step-by-step guide with more worked examples, the rule of 72 and how compounding works against you on debt, read compound interest explained. To see what growth means for a US retirement account, try the 401(k) calculator; for borrowing, the loan calculator shows how interest adds to a loan. The percentage calculator helps with quick percentage changes, and all money tools are in salary and money calculators.
Privacy
Everything is calculated in your browser and nothing you type is sent to a server. Your inputs (amounts, rate, compounding, term, contribution timing, increase, inflation and currency) are kept in this browser's local storage so the calculator opens the way you left it.
Frequently asked questions
What is the compound interest formula?
A = P(1 + r/n)nt, where P is the starting amount, r the annual rate as a decimal, n how many times a year interest is added and t the number of years. Regular deposits add PMT × ((1 + i)N − 1) / i, the future value of a series. The calculator shows both with your numbers.
How much will $10,000 grow in 10 years?
As an example, at 5% a year compounded monthly, $10,000 grows to about $16,470.09 in 10 years, so it earns about $6,470 in interest. At 7% compounded monthly it would reach about $20,096.61. Returns are not guaranteed for investments, so try a few rates.
What is the difference between APR and APY?
APR is the nominal yearly rate (for loans it also includes some fees). APY, or AER, is the effective yearly rate once compounding is included. 5% APR compounded monthly is an APY of 5.116%. Savings accounts are best compared on APY or AER.
Does compounding frequency matter much?
Less than most people think. 1,000 at 5% for 10 years becomes 1,628.89 with yearly compounding and 1,648.66 with daily compounding. The rate, the time and how much you add each month matter far more.
Should contributions be at the start or end of the period?
Choose what matches your saving. Paying at the start gives each deposit one extra period of interest: 100 a month for 10 years at 5% compounded monthly grows to 15,528.23 at the end of each month and 15,592.93 at the start.
Is this compound interest calculator free?
Yes. It is free with no sign-up and runs entirely in your browser. It gives estimates for illustration, not financial advice.
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