How to calculate simple and compound interest
Take the amount in the answer above: $25,000 at 5.00% a year, with interest added once a year, for 5 years.
- Simple interest is paid on the starting amount only and never added to the balance, so it is the amount times the annual rate times the number of years. $25,000 × 5.00% × 5 = $6,250
- The textbook formula for compound interest is P × (1 + r ÷ n)^(n × t), where P is the starting amount, r the annual rate, n the number of times a year interest is added and t the number of years. Here n × t is 5. $25,000 × (1 + 5.00%)^5 = $31,907.04
- This calculator works month by month in whole cents. Each month the balance earns the annual rate divided by twelve, rounded to the cent, and that interest waits, earning nothing itself, until it is added to the balance at the end of month 12. From month 1 to month 12: $25,000 × 5.00% ÷ 12 = $104.17 a month 12 × $104.17 = $1,250.04 $25,000 + $1,250.04 = $26,250.04
- The same steps repeat on each new balance to the end of the term. After 5 years the balance is $31,907.20, which is $0.16 more than the formula's $31,907.04, because this calculator rounds each month's interest to the cent and the formula never rounds. $31,907.20 − $31,907.04 = $0.16
- Everything above the starting amount is compound interest, and what compounding adds is its difference from simple interest. $31,907.20 − $25,000 = $6,907.20 $6,907.20 − $6,250 = $657.20
That is where the balance of $31,907.20 and the $6,907.20 of interest in the answer come from.
Simple interest and compound interest
Simple interest is the rate applied to the original amount, every period, forever. Ten thousand at five per cent earns five hundred in year one, five hundred in year two, and five hundred in year twenty. The interest never earns anything itself.
Compound interest adds each period's interest to the balance, so the next period earns on a larger amount. Year one is the same five hundred. Year twenty is not.
This page runs both on the same money so the gap is a figure rather than a slogan. Over a year the two are within a few cents of each other. Over five years the gap is noticeable. Over twenty it is larger than the original amount at many rates.
Where each one is actually used
Compound interest is the normal case for anything you hold: savings accounts, deposits, bonds where coupons are reinvested, and any investment measured by total return.
Simple interest is not a historical curiosity. It is how interest on many consumer instruments is calculated between payment dates, how statutory interest on late payments and on court judgments is usually defined, and how some fixed-term deposits that pay interest out rather than rolling it up behave. Anywhere the interest leaves the account rather than staying in it, simple interest is the right model.
That is the useful way to tell them apart: ask whether the interest stays where it was earned. If it does, compound. If it is paid away, simple.
The rate is what matters, not the compounding
It is tempting to treat compounding frequency as the lever. It is not. Going from yearly to monthly compounding is worth a small fraction of a percentage point of effective return; going from four per cent to five is worth a full point. Compare rates first and cycles second.
The other thing that outweighs the cycle is time. Doubling the term does far more than any change of compounding frequency at any rate this calculator accepts.
Common questions
Over one year the two are nearly identical. Is that right?
Yes. With interest added once a year there is nothing to compound inside the first year, so the two definitions agree apart from rounding. This page earns interest monthly and rounds each month to the cent, so the two can sit a few cents apart in year one, and the difference can fall either way. From the second year on, compounding wins outright.
Does the simple interest figure include my deposits?
No, and deliberately. Simple interest on a stream of deposits would need a convention for how long each one had been sitting there, and there is more than one defensible answer. The comparison is on the starting amount alone, which is the case where both definitions are unambiguous.
Is this interest earned or interest owed?
The arithmetic is identical either way; only the sign of your feelings changes. For a loan with a repayment schedule, the loan calculator is the right page, because there the balance falls as you pay it down and the interest falls with it.
What about tax on the interest?
Not included. Interest is taxed differently by country and by account type. If yours is taxed at source, entering the after-tax rate gives a reasonable approximation.
Is anything I type stored?
No. The calculation runs in your browser, nothing is sent anywhere, and the access log for this site drops the query string.
Sources
There is no official table behind a savings projection. What these documents pin down is the measure this tool deliberately does not compute, the one that folds compounding into a single advertised number:
How these figures are worked out
The balance is built month by month in whole cents rather than from a power formula. Each month earns the annual rate divided by twelve on the balance at that moment, rounded to the nearest cent in a single division, and that interest waits without earning anything itself until the compounding date folds it into the balance. The last month of the term always compounds, so a term that ends part way through a period is still paid what it earned. This is why yearly compounding here does not pay a full year of interest on a deposit made in December, and why the figures can sit a few cents from a textbook formula that rounds only once.
It leaves out tax on interest, fees, inflation and any withdrawal along the way.