What does an APY calculator work out?
An interest rate on its own does not say how much you earn in a year, because interest can be added once a year or many times. The annual percentage yield, APY, folds the compounding in and gives one yearly figure. This calculator works it out three ways:
- Rate to APY: from a nominal rate and how often interest compounds, with continuous compounding as the limit case.
- APY to rate: the nominal rate an account must pay at a given frequency to deliver an APY.
- From interest paid: the APY implied by the interest a deposit actually earned over a number of days.
On the default inputs, 5% compounded daily is an APY of 5.127%, and a $10,000 balance earns $512.67 in a year.
What is the APY formula?
For a nominal rate r compounded m times a year, APY = (1 + r / m)^m - 1. With daily compounding at 5%, that is (1 + 0.05 / 365)^365 - 1 = 5.1268%.
As m grows the APY approaches a limit, reached when interest compounds continuously: APY = e^r - 1, where e is about 2.71828. At 5% that gives 5.1271%, only 0.00036 percentage points above daily compounding. At 10%, monthly compounding gives 10.471%, daily 10.516% and continuous 10.517%. Continuous compounding is mostly a modeling device in finance; it marks the ceiling that more frequent compounding approaches.
The reverse formulas solve for r: r = m x ((1 + APY)^(1/m) - 1), or r = ln(1 + APY) for continuous compounding.
APY at every compounding frequency
Here is one nominal rate and one APY run through each frequency on the calculator's menu:
| Compounded | APY from a 5% nominal rate | Nominal rate for a 5% APY |
|---|---|---|
| Annually | 5.0000% | 5.0000% |
| Every six months | 5.0625% | 4.9390% |
| Quarterly | 5.0945% | 4.9089% |
| Monthly | 5.1162% | 4.8889% |
| Weekly | 5.1246% | 4.8813% |
| Daily | 5.1268% | 4.8793% |
| Continuously | 5.1271% | 4.8790% |
The two columns are mirror images. More frequent compounding lifts the APY for a given rate, and lowers the rate needed for a given APY. Most of the gain comes in the first steps: going from annual to monthly adds 0.116 points at 5%, and everything after that adds about 0.011 more.
How is APY defined in US law?
In the US, the rule is Regulation DD (Truth in Savings), 12 CFR part 1030. As published on the Consumer Financial Protection Bureau's site when checked in November 2026, section 1030.2 defines the annual percentage yield as a percentage rate reflecting the total amount of interest paid on an account, based on the interest rate and the frequency of compounding for a 365-day period, calculated by the rules in Appendix A. The same section defines the interest rate as the annual rate paid that does not reflect compounding, which is the nominal rate on this page.
Appendix A, Part I gives the general formula APY = 100 x [(1 + interest / principal)^(365 / days in term) - 1], based on the actual number of days in the term. Its own example of a six-month certificate of deposit, $30.37 of interest on $1,000 over 182 days, gives 6.18%, and those are this calculator's defaults on the From interest paid tab. Over exactly 365 days the formula reduces to interest divided by principal: the appendix's $61.68 on $1,000 is 6.17%.
What is AER in the UK, and is it the same as APY?
AER stands for annual equivalent rate. It answers the same question as APY: what a savings rate would be if interest were added once a year. The arithmetic is identical, so a 4% AER and a 4% APY describe the same yearly growth, and every result on this page can be read as either.
The UK Code of Broadcast Advertising, as published on the Advertising Standards Authority's site in November 2026, sets the rule for adverts: under rule 14.7.2, broadcast advertisements quoting a savings rate must use the AER and the contractual rate. When you compare accounts, compare AER with AER. A rate described as gross or contractual may be the nominal rate before compounding, which belongs in the first tab here, not the second.
Worked examples in pounds, euros and dirhams
The APY is a percentage, so it is the same in any currency; the balance shows what it means in money. These rates are examples, not offers.
| Account | Nominal rate and compounding | APY or AER | Interest in a year |
|---|---|---|---|
| Pounds | 3.9%, monthly | 3.970% | £397.05 on £10,000 |
| Euros | 3%, quarterly | 3.034% | €606.78 on €20,000 |
| Dirhams | 4%, monthly | 4.074% | AED 2,037.08 on AED 50,000 |
In reverse, a 4% AER comes from 3.9414% compounded quarterly, 3.9285% monthly or 3.9223% daily. The Rate to APY tab shows the money figure for any balance you enter, formatted in the currency you pick.
How do you calculate APY in Excel or Google Sheets?
Microsoft documents two functions for this. EFFECT(nominal_rate, npery) returns the effective annual rate, and its help page shows =EFFECT(0.0525, 4) returning 0.0535427: 5.25% compounded quarterly is an APY of about 5.354%. NOMINAL(effect_rate, npery) goes the other way. Both truncate npery to a whole number and return an error for a rate of zero or less.
For daily compounding, =EFFECT(0.05, 365) gives the 5.1268% in the table above. Neither function handles continuous compounding; use =EXP(0.05)-1 for the APY and =LN(1+0.05) for the rate. For the Regulation DD formula, =(1+30.37/1000)^(365/182)-1 returns 6.18% once formatted as a percentage.
APY, APR and simple interest: common mix-ups
- APY is not APR. APR is a measure for borrowing, with its own definition. This page is about the yearly growth of a deposit.
- Compounding twice. An APY already includes compounding. Entering it as a nominal rate in another calculator and compounding again overstates growth.
- Annualizing a short term by simple multiplication. $30.37 on $1,000 over 182 days is 6.09% a year by simple scaling but 6.18% as an APY, because the second half-year would earn interest on the first.
- Expecting a big gain from daily compounding. At 5%, daily beats monthly by 0.011 points.
- Comparing a quoted rate with an APY. Convert both to APY first, using the tabs here.
What this calculator leaves out
The figures assume one rate held for a full year with interest left in the account. They do not include tax on interest, fees, minimum balance rules, tiered rates or a rate that changes partway through, and the From interest paid tab follows only the general formula in Part I of Appendix A, not the special cases the regulation sets out for tiered or stepped rates or for statements. To grow a balance over several years with deposits, use the savings calculator; for a term deposit with an early withdrawal penalty, use the CD calculator.
Glossary
APY (annual percentage yield): the yearly rate including compounding, as defined for US deposit accounts. AER (annual equivalent rate): the UK term for the same idea. Nominal rate: the yearly rate before compounding, called the interest rate in Regulation DD. Compounding frequency: how often interest is added and starts earning interest itself. Continuous compounding: the limit as compounding becomes constant, giving e^r - 1. Effective annual rate: the general finance name for APY or AER.
Frequently asked questions
How do you calculate APY?
APY = (1 + r / m)^m - 1, where r is the nominal rate as a decimal and m the number of times interest compounds each year. A 5% rate compounded daily gives (1 + 0.05 / 365)^365 - 1 = 5.127%.
What is the APY of 5% compounded monthly?
5.116%. Compounded quarterly it is 5.095%, daily 5.127% and continuously 5.127% as well, to three decimals. The differences between frequencies are small next to the rate itself.
How do I convert APY to an interest rate?
Use r = m x ((1 + APY)^(1/m) - 1). A 5% APY compounded daily needs a nominal rate of 4.879%; compounded monthly it needs 4.889%. The second tab of this calculator does this for every frequency.
What is the formula for APY with continuous compounding?
APY = e^r - 1, where e is about 2.71828. At 5% that is 5.1271%, the highest APY any compounding frequency can reach at that rate. The reverse is r = ln(1 + APY).
Is AER the same as APY?
They are the same calculation under different names: AER is used in the UK and APY in the US. Both state the yearly rate with compounding included, so the results here apply to either.
How is APY calculated on a CD with a term shorter than a year?
Regulation DD's general formula is APY = 100 x [(1 + interest / principal)^(365 / days in term) - 1]. Its example of $30.37 earned on $1,000 over 182 days gives an APY of 6.18%.
What is the difference between APY and APR?
APY describes what a deposit earns in a year with compounding. APR is a measure for borrowing, with its own definition. They answer different questions, so a loan's APR and an account's APY are not directly comparable.
How do I calculate APY in Excel?
Use =EFFECT(nominal rate, periods per year), for example =EFFECT(0.05, 365) for daily compounding. =NOMINAL(APY, periods per year) reverses it, and =EXP(rate)-1 gives the continuous case.
Does daily compounding earn much more than monthly?
Very little. At 5%, daily compounding gives an APY of 5.1268% against 5.1162% for monthly, which is about $1.06 a year more on $10,000.
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- Regulation DD (Truth in Savings), 12 CFR 1030.2, definitions of annual percentage yield (total interest paid, based on the interest rate and the frequency of compounding for a 365-day period) and interest rate (the annual rate that does not reflect compounding); Consumer Financial Protection Bureau site. Checked 14 November 2026.
- Regulation DD, Appendix A to part 1030, Part I, APY = 100 [(1 + interest / principal)^(365 / days in term) - 1]; examples: 61.68 on 1,000 for 365 days = 6.17%; 30.37 on 1,000 for 182 days = 6.18%. Checked 14 November 2026.
- UK Code of Broadcast Advertising (BCAP Code), section 14, rule 14.7.2, advertisements quoting a savings rate must use the Annual Equivalent Rate (AER) and the contractual rate; Advertising Standards Authority site. Checked 14 November 2026.
- Microsoft Support, EFFECT and NOMINAL functions, EFFECT(nominal_rate, npery) and NOMINAL(effect_rate, npery); npery truncated to an integer; =EFFECT(0.0525, 4) returns 0.0535427. Checked 14 November 2026.