APY Calculator

APY shows the true yearly return after compounding. Compare accounts fairly by converting rate plus frequency to APY.

How the APY Calculator works

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Example calculation

The examples below take three different nominal rates and show how the same headline number produces different yields once frequency changes - and how to run the conversion backward. Every figure is recomputed.

Example 1 - a 5% nominal rate compounded monthly. Here r = 0.05 and n = 12. The periodic rate is 0.05 / 12 = 0.0041667. Then (1.0041667)¹² = 1.051162, so APY = 5.1162%. The same 5% compounded daily (n = 365) gives 5.1267%, and compounded only annually it stays at exactly 5.0000%. The lesson: the headline rate alone is not your yield.

Example 2 - a 4.5% nominal rate compounded daily. With r = 0.045 and n = 365, the periodic rate is 0.0001233. Raising (1.0001233)³⁶⁵ gives 1.046025, so APY = 4.6025%. On a $25,000.00 deposit, that effective yield earns $1,150.62 in the first year versus $1,125.00 at a flat 4.50% with no compounding - a $25.62 difference created purely by compounding.

Example 3 - back-solving the nominal rate from a 5.10% APY compounded monthly. Using r = n × ((1 + APY)^1/n - 1) with n = 12: (1.051)^1/12 = 1.0041538, minus 1 is 0.0041538, times 12 = 0.049845, so the nominal rate is 4.9845%. This is the exact step that lets you compare a bank quoting 5.10% APY against one quoting a 4.99% nominal rate - convert one to the other's basis first.

Nominal rate	Frequency	n	APY
5.00%	Annual	1	5.0000%
5.00%	Monthly	12	5.1162%
5.00%	Daily	365	5.1267%
4.50%	Daily	365	4.6025%
5.10% APY	Monthly (back-solved)	12	4.9845% nominal

Notice the gap between monthly and daily on the same 5% rate is only about 0.0106 percentage point - frequency matters, but its returns shrink fast past monthly, which is exactly why this converter exists: to expose how little the marketing word "daily" actually buys you.

Tips for using the APY Calculator

• Compare offers by APY, never by the nominal rate, because two accounts with the same headline rate but different compounding pay different amounts; this converter exists precisely to put them on equal footing.
• When a bank quotes only a nominal rate and a competitor quotes APY, back-solve the nominal one to APY (or convert the APY to nominal) before comparing - never compare a nominal figure against an APY directly, because the nominal one is always quietly worth slightly more once compounded.
• Stop chasing daily over monthly compounding; on a 5% rate the difference is only about 0.0106 percentage point, so a higher nominal rate beats a more frequent compounding schedule almost every time.
• Treat continuous compounding (e^r - 1) as the ceiling: a 5% continuous rate yields 5.1271%, only 0.0004 percentage point above daily's 5.1267%, so any account advertising 'continuous' compounding gives you essentially nothing over daily.
• To convert a loan's APR into the effective rate you truly pay on a carried balance, use APY = (1 + APR/n)^n - 1 with the loan's compounding frequency; a 6% APR compounded monthly costs you 6.1678% effectively, higher than the headline.
• Round the way the Truth in Savings Act requires - APY is disclosed to two decimal places, so 5.1162% is shown as 5.12%; do not assume a flat '5.12% APY' tells you the underlying nominal rate without back-solving it.
• Use this converter on bond and CD quotes that state a 'coupon rate' compounded semiannually: a 6% semiannual coupon is actually a 6.0900% effective yield, which matters when comparing against a monthly-compounding savings account.
• When introductory rates or tiered balances change the rate partway through a year, convert each tier separately; this tool assumes one constant rate for the full year, so blended periods need a weighted approach you compute by hand.
• Ignore APY on accounts you will not hold for a full year - APY is an annualized figure, so a 60-day promo paying '5.00% APY' does not mean you pocket 5%; you earn roughly the two-month slice of it.
• Reverse the logic to audit a lender: if a credit card states a daily periodic rate, multiply by 365 to find the nominal APR, then run it here to see the effective annual cost compounding actually imposes on a revolving balance.

APR vs APY: the difference that decides which account wins

APR is a nominal, non-compounded rate, while APY is the effective rate after compounding - APY is always equal to or higher than APR for the same nominal rate. APR (annual percentage rate) is the headline number; APY (annual percentage yield) is what you actually earn or pay once interest is added to the balance and then earns interest on itself. The more frequently compounding happens, the wider the gap.

The table below holds the nominal rate at 6% and only changes frequency, so every row shares the same APR but lands on a different APY:

APR (nominal)	Compounding	APY (effective)
6.00%	Annual	6.0000%
6.00%	Semiannual	6.0900%
6.00%	Quarterly	6.1364%
6.00%	Monthly	6.1678%
6.00%	Daily	6.1831%
6.00%	Continuous	6.1837%

For savings, you want the highest APY. For loans, you want the lowest APY-equivalent cost. This converter stops at the rate - to turn the converted rate into dollars over time on a real balance, hand it to the compound interest calculator; to convert a loan's APR into a monthly payment, use the loan calculator.

Why more frequent compounding raises APY (and why the gains stall)

More frequent compounding raises APY because interest is added to the balance sooner, so it starts earning its own interest earlier in the year - but the gains shrink rapidly and hit a hard ceiling at continuous compounding. Each time you split the year into more periods, the periodic rate gets smaller but it acts more often. The net effect is positive, yet it follows the law of diminishing returns.

Watch a 3% nominal rate climb as frequency increases: annual = 3.0000%, quarterly = 3.0339%, monthly = 3.0416%, daily = 3.0453%, and the mathematical limit (continuous, e^0.03 - 1) = 3.0455%. The jump from annual to monthly adds 0.0416 of a percentage point; the jump from daily all the way to continuous adds barely 0.0001. That is why marketing language like 'compounded daily' sounds impressive but moves the real yield almost nothing past monthly. A rate that is even one-tenth of a point higher will beat a more frequent compounding schedule every time - the central reason this converter is built around the rate, not the schedule.

The Truth in Savings Act: why APY exists at all

U.S. depository institutions are required to disclose APY (not just the nominal rate) on savings products because of the federal Truth in Savings Act of 1991, implemented through Regulation DD. Before this law, institutions advertised rates using inconsistent compounding assumptions, making it nearly impossible for consumers to compare accounts honestly. The law forced a single standardized number - APY - calculated with a uniform formula and disclosed to two decimal places.

That is why a deposit ad must lead with APY, and why APY is the figure you should anchor on when shopping. The flip side is that the underlying nominal rate is often buried or omitted. This converter lets you recover it: enter the disclosed APY, choose the compounding frequency, and back-solve to the nominal rate - something a balance projector cannot do. For background on how regulators define and police these terms, see the external reference linked below. If you are evaluating a fixed-term product instead of an open savings account, the CD calculator projects the actual maturity balance once you have the right rate.

How to calculate APY by hand and in Excel

In Excel or Google Sheets, the built-in function is =EFFECT(nominal_rate, npery), which returns APY directly from a nominal rate and the number of compounding periods. For a 5% nominal rate compounded monthly, type =EFFECT(0.05, 12) and you get 0.051162, or 5.1162%. To go the other direction and recover the nominal rate from a known APY, use =NOMINAL(0.0512, 12), which returns about 0.050036 (5.0036% nominal for a 5.12% APY).

If you prefer a raw formula instead of the financial functions, type =(1 + 0.05/12)^12 - 1 for the same monthly result, or =EXP(0.05) - 1 for the continuous-compounding case (5.1271%). To back-solve manually without NOMINAL, use =12*((1 + 0.051)^(1/12) - 1), which returns 0.049845 (4.9845% nominal from a 5.10% APY).

By hand the steps are: divide the nominal rate by n, add 1, raise to the power n using a calculator's y^x key, subtract 1, and multiply by 100. Keep at least six decimal places during the calculation so rounding does not distort the two-decimal disclosed figure - a flat 5.12% APY back-solves to a different nominal rate depending on whether you carried six decimals or two.

Is this APY good? Benchmark reference numbers

Whether an APY is competitive depends entirely on the prevailing federal funds environment, but the structural relationships are constant: high-yield savings and CDs sit well above traditional brick-and-mortar savings, which often pay a fraction of a percent. Use these reference relationships rather than a fixed 'good number,' because rates move with the broader market.

• Traditional savings accounts have historically paid very low APYs, frequently well under 0.50%, regardless of the rate environment.
• High-yield online savings and money market accounts typically track close to the federal funds rate and are the benchmark to beat for liquid cash.
• CDs usually offer a modest premium over savings in exchange for locking your money for a fixed term.

A practical test built around this converter: compute the APY of the offer in front of you (or back-solve its nominal rate to confirm the disclosure), then compare it against a current high-yield savings benchmark you can verify today. If a 'premium' account's APY does not beat plain high-yield savings, the label is marketing. Because rates change constantly, confirm the live figure before deciding - and remember APY only tells you the rate, not whether the balance grows enough to hit a goal. For that, pair it with the savings goal calculator.

Advanced uses: continuous compounding and APY-to-APR for loans

Continuous compounding (APY = e^r - 1) and APY-to-APR conversion are the two power moves this tool supports beyond simple savings shopping. Continuous compounding is the theoretical limit where interest is added at every instant. For a 5% nominal rate it yields 5.1271%, only 0.0004 percentage point above daily's 5.1267% - confirming that 'continuous' is a textbook concept, not a meaningful real-world advantage. It appears mostly in finance models and option pricing rather than retail accounts.

The APY-to-APR direction matters for borrowing. Lenders quote APR (nominal), but the rate you effectively pay on a revolving balance is the compounded equivalent. A 6% APR card compounded monthly actually costs 6.1678% per year on a carried balance - higher than the headline APR. Knowing this lets you compare a card's true cost against the true yield of an investment on a single basis. To see how an effective rate translates into total interest on an amortizing debt, run it through the loan calculator, and to model what the same rate could earn instead of cost, use the investment calculator.

Common mistakes when working with APY

The most damaging mistake is comparing a nominal rate from one account against an APY from another - always convert both to the same basis first with this tool. A '5.00% nominal' account and a '5.00% APY' account are not equal; the nominal one is actually slightly better once compounded. Below are the errors that cost real money.

• Treating APY as a guaranteed payout for any holding period. APY is annualized. A 60-day promo at '5.00% APY' does not pay 5%; it pays roughly the two-month slice.
• Assuming daily compounding dramatically beats monthly. On a 5% rate the difference is about 0.0106 percentage point - effectively a rounding error.
• Forgetting that APY ignores fees. A monthly maintenance fee can erase the entire yield advantage; the converted rate is not the net return.
• Using APY where you need a balance projection. This converter outputs a rate, not a future value. To project growth over multiple years on a specific deposit, switch to the compound interest calculator.
• Rounding too early. Cutting to two decimals mid-calculation can shift the final APY; keep six decimals until the last step.

APY quick-reference: how nominal rate plus compounding frequency converts to effective annual yield

The table below shows the APY a single nominal rate produces under each compounding frequency, using APY = (1 + r/n)ⁿ - 1. Notice that more frequent compounding raises the yield, but the gap is small at normal deposit rates; the continuous column (e^r - 1) is the mathematical ceiling. Every figure was recomputed for this table.

Nominal rate	Annually (n=1)	Quarterly (n=4)	Monthly (n=12)	Daily (n=365)	Continuous
3.00%	3.0000%	3.0339%	3.0416%	3.0453%	3.0455%
4.00%	4.0000%	4.0604%	4.0742%	4.0808%	4.0811%
4.50%	4.5000%	4.5765%	4.5940%	4.6025%	4.6028%
5.00%	5.0000%	5.0945%	5.1162%	5.1267%	5.1271%
5.50%	5.5000%	5.6145%	5.6408%	5.6536%	5.6541%
6.00%	6.0000%	6.1364%	6.1678%	6.1831%	6.1837%

Use this APY Calculator to convert any rate, then the Savings Calculator or CD Calculator to project a balance.

Related on this site

Compound Interest Calculator · CD Calculator · Savings Calculator · Simple Interest Calculator · Savings Goal Calculator · Future Value Calculator

For a related deep dive, see CFPB on APR and APY.

APY Calculator — frequently asked questions

APR vs APY?

APR ignores compounding; APY includes it. APY is always equal to or higher than the nominal rate.

Why does frequency matter?

More frequent compounding produces a higher effective yield from the same nominal rate.

APR vs APY?

APR ignores compounding; APY includes it. Savers should compare APY.

Why do banks advertise APY?

It reflects the actual yearly earnings a saver receives.

How much does a $10,000 deposit at 4.50% APY earn in one year?

<p>A $10,000 deposit at 4.50% APY earns $450.00 in interest over one year, ending at $10,450.00.</p><p>Because APY already bakes in compounding, you simply multiply: $10,000 x 0.045 = $450.00 for a full year with no deposits or withdrawals. That is the whole point of APY - it states your true 12-month return so you do not have to redo the compounding math. To project multiple years or add monthly deposits, use the <a href="/savings-calculator/">Savings Calculator</a>.</p>

What APY does a 5% nominal rate become when compounded monthly versus daily?

<p>A 5% nominal rate becomes 5.1162% APY compounded monthly and 5.1267% APY compounded daily.</p><p>Using APY = (1 + r/n)ⁿ - 1: monthly gives (1 + 0.05/12)¹² - 1 = 5.1162%, and daily gives (1 + 0.05/365)³⁶⁵ - 1 = 5.1267%. The extra compounding frequency adds only about 0.0106 percentage point, so daily compounding is a minor edge, not a game-changer, at this rate. The continuous ceiling is 5.1271%.</p>

How do I convert APY back to the nominal interest rate?

<p>Back-solve with nominal r = n x ((1 + APY)^1/n - 1), where n is the compounding frequency.</p><p>For a 5.00% APY compounded monthly: r = 12 x ((1.05)^1/12 - 1) = 4.8889%. Compounded daily, the same 5.00% APY back-solves to 4.8793% nominal. The more often interest compounds, the lower the nominal rate needed to hit a given APY. This back-solve is the feature that separates a rate converter from a balance projector.</p>

What is the effective annual rate of a credit card with 24.99% APR?

<p>A 24.99% APR compounded daily has an effective annual rate of about 28.38%.</p><p>Credit card APR is a nominal rate, so its true cost rises once interest compounds. Using (1 + 0.2499/365)³⁶⁵ - 1 = 28.38%. A 19.99% APR card compounds to roughly 22.12% effective. That gap is why a carried balance costs more than the headline APR suggests. APY and effective annual rate use the same formula; banks just call it APY for savings and EAR for debt.</p>

How do I calculate APY in Excel?

<p>Use Excel's EFFECT function: =EFFECT(nominal_rate, compounding_periods).</p><p>For a 5% nominal rate compounded monthly, enter =EFFECT(0.05,12), which returns 0.051162 or 5.1162% APY - identical to the (1 + r/n)ⁿ - 1 hand formula. To go the other direction, =NOMINAL(0.0512,12) back-solves a 5.12% APY to about 5.0036% nominal. Both functions live in standard Excel and Google Sheets with no add-in required.</p>

What is the continuous-compounding APY of a 4.75% rate?

<p>A 4.75% nominal rate compounded continuously gives an APY of 4.8646%, using e^r - 1.</p><p>Continuous compounding is the mathematical limit as periods approach infinity: e^0.0475 - 1 = 4.8646%. On a $30,000.00 deposit that is $1,459.39 a year, versus $1,459.29 with daily compounding - a $0.10 difference. Continuous compounding is a textbook ceiling; real US savings accounts compound daily or monthly, so the practical gain over daily is essentially zero.</p>

How much more does $20,000 earn with daily compounding versus simple annual interest at 5%?

<p>At a 5% nominal rate, $20,000 earns $1,025.35 with daily compounding versus $1,000.00 with simple annual interest - a $25.35 difference in one year.</p><p>Daily compounding converts 5% nominal to 5.1267% APY, so $20,000 x 0.051267 = $1,025.35, while simple interest is just $20,000 x 0.05 = $1,000.00. The $25.35 edge is real but modest; compounding frequency matters far less than the rate itself and the balance.</p>

What is the Truth in Savings Act and why must banks disclose APY?

<p>The Truth in Savings Act (1991, Regulation DD) requires US depository institutions to disclose APY so savers can compare accounts on one standardized number.</p><p>Before the law, banks advertised nominal rates with different compounding schemes, making comparison nearly impossible. APY is defined by a uniform federal formula, so a 5.00% APY at one bank means the same yearly return as 5.00% APY at another, regardless of whether interest posts daily or monthly. That standardization is exactly what this APY Calculator reproduces and lets you reverse.</p>

Is the difference between quarterly and semi-annual compounding worth chasing on a $40,000 balance?

<p>On $40,000 at a 6% nominal rate, quarterly compounding yields $2,454.54 and semi-annual yields $2,436.00 - a difference of about $18.54 a year.</p><p>Quarterly converts 6% to 6.1364% APY; semi-annual gives 6.0900%. The $18.54 gap is real but tiny next to choosing a higher rate. Picking an account paying 0.25 points more would add about $100 on the same balance, so prioritize the rate first, then compare APY to settle ties.</p>

What nominal rate do I need to reach a 4.50% APY?

<p>To reach a 4.50% APY you need about a 4.4098% nominal rate compounded monthly, or 4.4020% compounded daily.</p><p>Back-solving with r = n x ((1 + APY)^1/n - 1): monthly gives 12 x ((1.045)^1/12 - 1) = 4.4098%, and daily gives 4.4020%. More frequent compounding lets a slightly lower nominal rate hit the same yield. If interest compounds only annually, the nominal rate and APY are identical at 4.50%.</p>

How much will $8,000 grow to at 5% APY over 5 years?

<p>$8,000 at 5% APY grows to $10,210.25 after 5 years, earning $2,210.25 in interest.</p><p>Because APY is already the annual compounded yield, multi-year growth is $8,000 x (1.05)⁵ = $10,210.25. Note this assumes the APY holds steady for all five years, which variable savings rates rarely do. For changing rates or regular contributions, model it with the <a href="/compound-interest-calculator/">Compound Interest Calculator</a>.</p>

Why is APY always higher than the nominal rate except when compounding annually?

<p>APY exceeds the nominal rate whenever interest compounds more than once a year, because you earn interest on previously credited interest; they are equal only when compounding is annual.</p><p>With annual compounding, n = 1, so (1 + r/1)¹ - 1 = r exactly. Add more periods and each one earns on a slightly larger balance, lifting the yield. For example, 4% nominal stays 4.0000% APY annually but rises to 4.0742% monthly. APY can never be below the nominal rate.</p>

Is a 5.00% APY actually better than a 5.10% nominal rate?

<p>No - a 5.10% nominal rate compounded monthly produces a 5.2209% APY, which beats a flat 5.00% APY.</p><p>Always compare on APY, never mix a nominal rate against an APY. Converting 5.10% nominal monthly: (1 + 0.051/12)¹² - 1 = 5.2209%, clearly higher than 5.00% APY. Conversely, a 5.10% APY back-solves to only about 4.9845% nominal compounded monthly. The headline number alone can mislead; the conversion settles it.</p>

Does a higher compounding frequency ever change which account is the better deal?

<p>Rarely - the rate almost always dominates, but on tied rates the more frequent compounding wins by a small margin.</p><p>Compare 3.5% nominal compounded daily against the same rate annually on $6,000: daily yields $213.71 (3.5618% APY) versus $210.00 (3.5000% APY), a $3.71 edge. Frequency only decides between accounts paying identical nominal rates. When rates differ by even a tenth of a point, that gap outweighs any compounding-frequency advantage, so check APY first.</p>

Guides & articles

• How to Convert a Nominal Rate to APY: The Effective Yield Formula
• How to Back-Solve the Nominal Rate From an APY

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