Compound interest calculator

How does compound interest work?

Compound interest is interest earned on interest. Each time interest is added to the balance, the next calculation starts from the larger figure, so growth speeds up the longer money stays put. Simple interest, by contrast, is only ever worked out on the original sum.

Take the default figures above: a starting amount of $10,000 at an assumed 7% a year. With simple interest it would earn $700 every year, or $7,000 over 10 years. Compounded monthly with no deposits, the same sum reaches $20,096.61, so interest on interest adds $3,096.61 on top of the $7,000. Add $200 a month and the balance after 10 years is $54,714, of which $34,000 is your own money and $20,714 is interest.

What is the compound interest formula?

For a single sum the formula is A = P x (1 + r / n)^(n x t), where P is the starting amount, r the annual rate as a decimal, n the number of times interest is compounded each year, and t the number of years.

Regular deposits need a second part. If you pay D each period, p times a year, the deposits grow to D x ((1 + rc)^(p x t) - 1) / rc, where rc is the rate for one deposit period. This calculator sets rc = (1 + r / n)^(n / p) - 1, so a monthly deposit into a daily-compounded account earns exactly what the account pays, with no rounding of the rate. When deposits are paid at the start of each period, the deposit part is multiplied by (1 + rc) once more.

The total balance is the two parts added together. Open Show the working under the result to see both parts with your own numbers, to two decimal places.

Worked examples in three currencies

The arithmetic is identical in every currency. Only the formatting changes, and the calculator never converts one currency into another.

In the dirham example, AED 180,000 goes in over 15 years and interest makes up almost a third of the final balance. Pick any of the 24 currencies in the selector and the symbols, separators and decimals follow the convention of your browser, so a balance in Japanese yen shows no decimals.

How often is interest compounded, and does it matter?

More frequent compounding adds a little more, but far less than people tend to expect. Here is $10,000 left for 10 years at a 7% annual rate, with only the compounding frequency changed:

Going from yearly to monthly compounding adds about $425 over the decade. Going from monthly to daily adds about $40 more. The rate itself and the number of years move the result far more than the frequency does, which is why the chart below the calculator is worth a glance before comparing two accounts on frequency alone.

Monthly or yearly deposits, at the start or the end?

Two settings change the answer more than most people realize. The first is timing. Paying the $200 at the start of each month instead of the end gives every deposit one more month of interest. On the default inputs that lifts the 10-year balance from $54,714 to $54,916, about $202 more for the same money.

The second is how often you pay. Putting in $2,400 once at the end of each year, rather than $200 every month, ends at $53,617 instead of $54,714, because each month's money waits longer before it starts earning. Deposit frequency and compounding frequency are separate settings here: you can pay monthly into an account that compounds daily, quarterly or yearly. Monthly deposits into an account that compounds only once a year finish at $53,882 on the same inputs.

APR, APY and AER: which rate are you looking at?

A nominal annual rate tells you the rate before compounding. The effective annual rate tells you what one year of compounding actually produces, and that is the figure to compare between accounts. In the US, savings products quote it as APY (annual percentage yield). In the UK the same idea is called AER (annual equivalent rate). Loans often quote an APR, which is a different measure that also folds in some fees.

The calculator shows the effective annual rate for whatever you enter: (1 + r / n)^n - 1. A 7% rate compounded monthly is 7.229% effective; compounded daily it is 7.250%. If an account already quotes an APY or AER, enter that figure and choose annual compounding, so the effect of compounding is not counted twice.

How do you calculate compound interest in Excel or Google Sheets?

Both use the same function: =FV(rate per period, number of periods, payment, present value), with money you pay in entered as a negative number. For the default example, =FV(0.07/12, 120, -200, -10000) returns 54,713.58, the same figure as the calculator. Add 1 as a fifth argument for deposits at the start of each period.

FV assumes the payment period and the compounding period are the same. For a daily-compounded account with monthly deposits, first convert the rate with (1 + 0.07/365)^(365/12) - 1 and use that as the rate per period, which is exactly what this calculator does for you.

For a quick mental check there is the rule of 72: divide 72 by the rate to estimate the years it takes to double money. At 7% that gives 10.29 years, against an exact 10.24 years with annual compounding.

What this calculator leaves out

The result is arithmetic on a fixed rate, and real balances rarely follow one. Savings rates change, investment returns vary from year to year and can be negative, and the order of good and bad years matters once you are paying in or drawing out. Treat the rate here as an assumption to test, not a figure anyone can promise.

The calculator also ignores tax on interest, account fees and withdrawals, all of which depend on where you live and the account you hold. To see the effect of rising prices, enter an inflation rate under Deposit timing and inflation: on the default inputs, 3% inflation a year means $54,714 in 10 years buys roughly what $40,712 buys today.

Common mistakes with compound interest

• Entering a monthly rate as an annual one. A card or loan quoted at 1.5% a month is about 18% a year before compounding, not 1.5%.
• Counting compounding twice. If a bank already quotes APY or AER, choose annual compounding.
• Comparing accounts on frequency instead of rate. As the table above shows, the frequency is worth tens of dollars where the rate is worth thousands.
• Forgetting deposit timing. Start and end of period give different answers, and spreadsheet functions default to the end.
• Reading a long projection as a forecast. Over 30 years the default inputs reach $325,159 from $82,000 paid in, but only if the rate held for all 30 years.

Glossary

Principal: the starting amount. Compounding frequency: how many times a year interest is added to the balance. Effective annual rate (APY or AER): the yearly growth rate once compounding is counted. Nominal rate: the quoted annual rate before compounding. Future value: what a sum and its deposits are worth at the end of the period. Real value: a future amount restated in today's purchasing power after inflation.

Frequently asked questions

Courses where compounding meets the markets

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