To convert a nominal interest rate to APY (annual percentage yield), use the formula APY = (1 + r/n)n - 1, where r is the stated annual rate as a decimal and n is the number of compounding periods per year. A 5.00% nominal rate compounded monthly, for example, converts to an APY of 5.1162%. The nominal rate tells you the headline number; the APY tells you what you actually earn once compounding is counted. The fastest way to run the conversion is our APY calculator, but the math below is simple enough to do on any phone.
This guide is about one specific job: turning a quoted nominal rate plus a compounding frequency into a single, honest effective yield you can compare across accounts. It is not about projecting a balance over five years - for that, use a savings calculator or a CD calculator. Here we stay on the rate itself: the formula, why frequency matters, a full conversion table you can reuse, and the continuous-compounding edge case that sets the ceiling on any yield.
Nominal rate vs APY: what each number means
A nominal rate is the simple, un-compounded annual rate a bank quotes; APY is that same rate after compounding is folded in, so APY is always equal to or higher than the nominal rate. They only match when interest compounds exactly once a year.
- Nominal rate (r): the stated annual rate, sometimes called the periodic rate annualized or the "interest rate." It ignores the effect of earning interest on interest within the year.
- Compounding frequency (n): how many times per year interest is calculated and added to the balance - 1 for annual, 4 for quarterly, 12 for monthly, 365 for daily.
- APY: the effective annual yield, expressing total first-year earnings as a single percentage that already includes compounding. This is the apples-to-apples number for comparing accounts.
The practical takeaway: never compare two accounts by their nominal rates if they compound differently. Convert both to APY first, then compare. A 4.55% rate compounded once a year (APY 4.55%) actually beats a 4.50% rate compounded monthly (APY 4.5940%) only barely - and you would never see that without converting.
The nominal-to-APY conversion formula
The conversion formula is APY = (1 + r/n)n - 1. Read it left to right: divide the nominal rate by the number of periods to get the periodic rate, add 1, raise the result to the power of n, then subtract 1 to strip the principal back out and leave only the yield.
Here is the formula applied to a 5.00% nominal rate (r = 0.05) compounded monthly (n = 12), step by step:
- Periodic rate: r/n = 0.05 / 12 = 0.0041667 (about 0.41667% per month).
- Add 1: 1 + 0.0041667 = 1.0041667.
- Raise to the 12th power: 1.004166712 = 1.051162.
- Subtract 1: 1.051162 - 1 = 0.051162, or 5.1162% APY.
That 0.1162 percentage-point gap between the 5.00% nominal rate and the 5.1162% APY is pure compounding. On a $10,000 balance it is the difference between $500.00 of simple interest and $511.62 of compounded interest in the first year - an extra $11.62 you earn just because interest was added monthly instead of once at year-end.
Nominal-to-APY conversion table
The table below converts the same 5.00% nominal rate at every common frequency, plus a 4.00% example, so you can see the pattern. APY rises as compounding gets more frequent, but the gains shrink fast - the jump from annual to monthly is large; the jump from monthly to daily is tiny.
| Nominal rate | Compounding | Periods (n) | APY | Interest on $10,000 |
|---|---|---|---|---|
| 5.00% | Annual | 1 | 5.0000% | $500.00 |
| 5.00% | Semiannual | 2 | 5.0625% | $506.25 |
| 5.00% | Quarterly | 4 | 5.0945% | $509.45 |
| 5.00% | Monthly | 12 | 5.1162% | $511.62 |
| 5.00% | Daily | 365 | 5.1267% | $512.67 |
| 5.00% | Continuous | infinite | 5.1271% | $512.71 |
| 4.00% | Annual | 1 | 4.0000% | $400.00 |
| 4.00% | Monthly | 12 | 4.0742% | $407.42 |
| 4.00% | Daily | 365 | 4.0808% | $408.08 |
Notice the ceiling. At a 5.00% nominal rate, even infinite (continuous) compounding only lifts the APY to 5.1271% - just 0.0004 points above daily. Once you are compounding daily, you have captured almost all the benefit there is. Anyone advertising "compounds every second" is selling a rounding error.
How to convert a nominal rate to APY in Excel or Google Sheets
Spreadsheets have a built-in function for this exact conversion: EFFECT. Type =EFFECT(nominal_rate, npery) where npery is the number of periods per year.
- Monthly:
=EFFECT(0.05, 12)returns 0.051162, or 5.1162%. - Quarterly:
=EFFECT(0.05, 4)returns 0.050945, or 5.0945%. - Daily:
=EFFECT(0.05, 365)returns 0.051267, or 5.1267%.
If you prefer the raw formula instead of EFFECT, enter =(1+0.05/12)^12-1 and format the cell as a percentage. EFFECT cannot model continuous compounding; for that, use =EXP(0.05)-1, which returns 0.051271.
The continuous-compounding edge case
Continuous compounding is the theoretical limit where interest is added an infinite number of times per year, and its APY is given by er - 1, where e is the constant 2.71828. It is the ceiling that ordinary compounding approaches but never quite reaches.
For a 5.00% nominal rate, continuous compounding yields e0.05 - 1 = 1.051271 - 1 = 5.1271% APY. Compare that to daily compounding at 5.1267% - the difference is four ten-thousandths of a percent, or about $0.04 on $10,000. Continuous compounding matters in finance theory and option pricing, but for a savings account it is effectively the same as daily. Knowing the formula is still useful: it instantly tells you the maximum APY any nominal rate can produce, so you can spot a quote that is mathematically impossible.
When the conversion changes your decision
Converting to APY changes a decision whenever two accounts quote different nominal rates and compound at different frequencies. A higher nominal rate with annual compounding can lose to a lower nominal rate that compounds monthly or daily, and only the APY reveals the winner. Banks already do this conversion for you - U.S. law requires deposit accounts to advertise APY, not the nominal rate, precisely so consumers can compare honestly. The Consumer Financial Protection Bureau oversees those disclosure rules.
The conversion is also the foundation for longer-term planning. Once you have the true APY, plug it into a compound interest calculator to project growth over many years, or use the Rule of 72 calculator to estimate how long that yield takes to double your money. The rate conversion comes first; everything else builds on it.
Try it yourself
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Open the APY Calculator →Frequently asked questions
- How do I convert a nominal interest rate to APY?
- Convert a nominal rate to APY with the formula APY = (1 + r/n) raised to the power n, minus 1, where r is the nominal rate as a decimal and n is the number of compounding periods per year. For a 5.00% nominal rate compounded monthly: (1 + 0.05/12) to the 12th power minus 1 = 5.1162% APY. In Excel, the shortcut is =EFFECT(0.05, 12).
- What is the difference between nominal rate and APY?
- The nominal rate is the stated annual rate before compounding; APY is that rate after compounding is included, so APY is always equal to or higher than the nominal rate. They are equal only when interest compounds once a year. A 5.00% nominal rate compounded monthly equals a 5.1162% APY, an extra $11.62 per year on $10,000.
- Does more frequent compounding always mean a higher APY?
- Yes, more frequent compounding always raises the APY for the same nominal rate, but the increases shrink quickly. At 5.00% nominal, annual compounding gives 5.0000% APY, monthly gives 5.1162%, and daily gives 5.1267%. The jump from annual to monthly is meaningful; from monthly to daily it is only about 0.01 points, roughly $1 a year on $10,000.
- What is the APY of a 5% rate compounded daily?
- A 5.00% nominal rate compounded daily produces an APY of 5.1267%. On a $10,000 balance that is $512.67 of interest in the first year, compared with $500.00 if the same rate compounded only once annually. The daily figure is within four thousandths of a percent of continuous compounding, which is the absolute maximum at that rate.
- What is continuous compounding and how is its APY calculated?
- Continuous compounding is the limit where interest is added infinitely often, and its APY equals e raised to the power r, minus 1, where e is about 2.71828. For a 5.00% nominal rate, that is e to the 0.05 minus 1 = 5.1271% APY. It is the highest APY any nominal rate can reach, but it barely exceeds daily compounding, so for savings accounts the two are practically identical.
- How do I calculate APY in Excel?
- Use the EFFECT function: type =EFFECT(nominal_rate, npery), where npery is periods per year. For a 5.00% rate compounded monthly, =EFFECT(0.05, 12) returns 5.1162%. You can also enter the raw formula =(1+0.05/12)^12-1 and format as a percentage. For continuous compounding, use =EXP(0.05)-1, which returns 5.1271%.
- Why do banks advertise APY instead of the nominal rate?
- Banks advertise APY because U.S. law requires it for deposit accounts, so consumers can compare accounts on one consistent number regardless of how often each compounds. Quoting only nominal rates would let an account with a higher headline rate but less frequent compounding look better than a truly higher-yielding account. APY removes that confusion by baking compounding into a single figure.
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