📈 Compound Interest Calculator
Calculate how monthly savings and interest compound over long-term investment horizons.
Compounding, contributions, and the part that does the real work
Compound interest is interest earned on interest. The balance grows, the interest is calculated on the larger balance, and the whole thing accelerates. Over a few years that is pleasant. Over a few decades it is the dominant force in the number, which is why starting early beats contributing more almost every time.
A = P(1 + r/n)nt + PMT × [ (1 + r/n)nt − 1 ] / (r/n)
The first term grows your starting balance. The second grows a stream of regular contributions. The calculator above runs both and shows how much of the final figure is money you deposited and how much the compounding produced.
Time beats amount
Two savers, both reaching 65, both earning 7% a year. Ana puts away $300 a month from 25 to 35 and then stops, contributing $36,000 in total. Bruno starts at 35 and contributes $300 a month for thirty years, putting in $108,000, three times as much.
| Saver | Contributes | Years contributing | Value at 65 |
|---|---|---|---|
| Ana (25–35) | $36,000 | 10 | $401,000 |
| Bruno (35–65) | $108,000 | 30 | $366,000 |
Ana stops before Bruno starts, pays in a third as much, and finishes ahead. The ten years she bought at the beginning were worth more than the twenty extra years of contributions he made at the end, because her money had the longest runway. This is the single most useful fact in personal finance and it is entirely a consequence of the exponent.
How much compounding frequency matters
Less than most people think. $10,000 at 6% for 20 years:
| Compounding | Final balance | Effective annual rate |
|---|---|---|
| Annually | $32,071 | 6.000% |
| Quarterly | $32,907 | 6.136% |
| Monthly | $33,102 | 6.168% |
| Daily | $33,198 | 6.183% |
| Continuously | $33,201 | 6.184% |
The whole range from annual to continuous is worth $1,130, about 3.5%. Moving the rate from 6% to 6.5% is worth $3,200. Chase the rate and the term; do not agonise over the frequency.
The rule of 72
Divide 72 by the annual percentage rate to get the rough number of years for money to double. At 6%, twelve years. At 9%, eight. At 3%, twenty-four. It is accurate to within a few months for rates between about 4% and 12% and it lets you sanity-check any growth claim in your head. If someone promises to double your money in two years, they are claiming a 41% annual return.
Inflation: the number that is missing
Everything above is nominal. If your portfolio grows 7% a year while prices rise 3%, your real return is closer to 3.9%, not 4% exactly, because the correct calculation divides rather than subtracts: (1.07 / 1.03) − 1. Over thirty years the difference between nominal and real is enormous: $300 a month at 7% reaches $366,000, but in today's purchasing power it is about $151,000.
For a long-horizon plan, run the calculation twice: once at your expected nominal return to see the account balance, and once at the real return to see what it will actually buy. The inflation calculator converts between the two.
A worked example
You have $15,000 saved and add $400 a month for 25 years at 6.5%, compounded monthly. The final balance is $374,900. Of that, $135,000 is money you put in and $239,900 is growth. The growth overtakes the contributions in year 14; from then on the account earns more each year than you add to it.
Frequently Asked Questions (FAQs)
What is a realistic rate of return to assume?
For a diversified stock portfolio, long-run historical averages sit around 7% to 10% nominal before inflation, with large swings in any given decade. For bonds, lower. For cash savings, whatever the account pays. Planning at 6% to 7% nominal is a common compromise; planning at 12% is planning on being lucky.
Should I contribute monthly or annually?
Monthly, if the choice is yours. Each contribution starts compounding sooner, which over thirty years is worth roughly 3% to 5% more than the same total paid once a year. It also removes the timing decision, which is where most people lose money.
What is the difference between APR and APY?
APR is the nominal annual rate before compounding. APY is what you actually earn over a year once compounding is applied. A 6% APR compounded monthly is a 6.17% APY. Savings products are usually advertised by APY and borrowing by APR, which flatters both.
Does this account for tax?
No. In a taxable account, interest and dividends are usually taxed as they are earned, which drags the effective rate down. In a tax-sheltered retirement account they are not, which is a large part of why those accounts compound so much faster. Reduce your assumed rate if the money is taxable.
What happens if returns are negative in some years?
This calculator assumes a steady rate. Real markets do not deliver one, and volatility reduces the compound result below what the arithmetic average suggests: a year of −20% followed by a year of +20% leaves you down 4%, not level. Treat the output as a central estimate, not a forecast.
Is compound interest the same as compound growth?
The arithmetic is identical. Interest is what a deposit account pays; growth is what an investment does. The formula does not care about the source, but the certainty does: a savings rate is contractual and an investment return is not.
How do I work out the rate I need to reach a target?
Rearrange for r, or use trial and error in the calculator. If you need $300,000 in 20 years from $50,000 plus $500 a month, you need about 5.6% a year. If the required rate comes out above 10%, the plan needs more contributions or more time rather than a riskier portfolio.