APR and APY are not the same number
A nominal rate is an annual rate quoted before you account for how often interest is added. If a rate of 5 percent is compounded monthly, the account credits 5/12 of a percent twelve times, and each credit earns interest afterwards. One year of that is not 5 percent, it is 5.116 percent. That second figure is the annual percentage yield.
| Compounding of a 5% nominal rate | APY | $10,000 after 10 years |
|---|---|---|
| Annually | 5.000% | $16,288.95 |
| Quarterly | 5.095% | $16,436.19 |
| Monthly | 5.116% | $16,470.09 |
| Daily | 5.127% | $16,486.65 |
Deposit accounts in the United States advertise APY, so two accounts quoting APY can be compared directly. Loans advertise APR, which is a nominal rate with certain fees folded in and no compounding assumption, so a 5 percent APR loan and a 5 percent APY savings account are not the same 5 percent. When you compare anything, check which of the two you are holding.
What this calculator assumes
Interest is applied monthly using the effective monthly factor implied by the compounding frequency you chose. For monthly compounding that is exactly the nominal rate divided by twelve. For annual, quarterly or daily compounding it is the twelfth root of the corresponding annual factor, which matches the stated frequency exactly at each year boundary and interpolates sensibly in between. Contributions default to the end of the month, which is the conservative assumption; moving them to the start adds roughly one extra month of growth over the whole term.
Tax, when you enter a rate above zero, is taken out of each year of interest at the end of that year, which is how a fully taxable account behaves and which slows the compounding slightly. The default is zero because there is no single right answer: interest in a tax-deferred retirement account is not taxed as it accrues, interest in an ordinary savings account generally is, and the rate depends on your total income and your jurisdiction. The calculator does not guess.
The rule of 72, and where it breaks
Divide 72 by the rate and you get roughly the number of years for money to double. At 6 percent, twelve years. At 9 percent, eight. It is accurate to within a few percent for rates between about 4 and 12, and it drifts at the extremes: at 1 percent the true answer is 69.7 years rather than 72, and at 20 percent it is 3.8 rather than 3.6. It is a mental check, not a result.
Fees are the term that is missing
Nothing above subtracts an expense ratio, an advisory fee, a platform charge or a spread. A 0.5 percent annual fee on a 7 percent return is not a 0.5 percent reduction in the final balance, it is closer to 12 percent of the gain over thirty years, because the fee compounds against you the same way the return compounds for you. If you are modelling an investment rather than a savings account, subtract the fee from the rate before you type it in, and treat everything the page prints as the arithmetic of that assumption rather than a claim about the future.
Questions people ask
Does $10,000 at 5% compounded monthly really reach $16,470.09 in ten years?
Yes. The exact figure is 10000 times (1 + 0.05/12) raised to the 120th power, which is $16,470.0950. Rounded to the cent that is $16,470.10, and $16,470.09 if you truncate rather than round, so both figures appear in circulation. The interest earned is about $6,470 on a $10,000 deposit, a 64.7 percent total gain over the decade, which is an annual percentage yield of 5.116 percent compounded ten times.
Why is my bank number slightly different?
Several small conventions differ between institutions. Some compound daily on a 365-day year, some on a 360-day year. Some credit interest monthly but calculate it on the average daily balance rather than the closing balance. Some round to the cent at each credit, which this calculator does not do until the display. Over a year these differences are typically a few dollars per ten thousand. If the gap is larger than that, the rate or the compounding frequency you entered is probably not the one the account actually uses.
Should contributions be set to the start or the end of the month?
End of month is the default and is the safer assumption, because it does not credit you with growth on money you have not deposited yet. Start of month gives every contribution one extra month of compounding. On $500 a month at 7 percent over twenty years the difference is around $1,500 on a balance near $260,000, so roughly half a percent. Pick whichever matches when the transfer actually leaves your account.
Can I use a market return like 7 or 10 percent here?
You can type it, but understand what the output then means. Compound growth at a fixed rate is a smooth curve; actual market returns are a sequence, and the order matters. Two sequences with identical averages produce different ending balances once you are adding or withdrawing money, because a contribution made before a bad stretch buys in at a different price than one made after. The number this page produces is what a constant rate would have given. It is a useful reference point and it is not a projection.