Effective Interest Rate Calculator
Savings & BankingTurn a nominal rate into the real one.
Rate & compounding
Money illustration
- At the stated rate$600
- Compounding bonus$17
First-year interest split: the stated rate does most of the work, and intra-year compounding adds the bonus slice on top.
Conversions use exact compound arithmetic; annual rates display to three decimals and periodic rates to four. Deposit accounts advertise APY rounded to two decimals under Regulation DD, so a bank's published figure can differ by a hair. No fees, taxes, deposits or withdrawals are modeled.
Effective rate by compounding schedule
One 6.00% quote, every crediting schedule side by side — the effective rate is what separates them.
| Frequency | Periods / yr | Periodic rate | Effective rate | vs nominal (pp) | Year-1 interest |
|---|---|---|---|---|---|
| Annually | 1 | 6.0000% | 6.000% | +0.000 | $600 |
| Semi-annually | 2 | 3.0000% | 6.090% | +0.090 | $609 |
| Quarterly | 4 | 1.5000% | 6.136% | +0.136 | $614 |
| MonthlySelected | 12 | 0.5000% | 6.168% | +0.168 | $617 |
| Weekly | 52 | 0.1154% | 6.180% | +0.180 | $618 |
| Daily | 365 | 0.0164% | 6.183% | +0.183 | $618 |
| Continuous | ∞ | — | 6.184% | +0.184 | $618 |
Lift above the nominal rate, by schedule (percentage points)
- Annually0.000 pp
- Semi-annually0.090 pp
- Quarterly0.136 pp
- Monthly0.168 pp
- Weekly0.180 pp
- Daily0.183 pp
- Continuous0.184 pp
Growth comparison
$10,000 left to grow over a 10-year horizon — the same quote credited yearly, on your schedule, and continuously.
What actually moves the needle?
Ending balance at the 10-year mark, changing one lever at a time.
- Current schedule$18,194
- +1 pp on the quote$20,097
- Daily compounding$18,220
- Continuous compounding$18,221
Switching to daily compounding is worth $26 over the horizon; one extra percentage point on the quote is worth $1,903. Negotiate the rate before you chase the frequency.
Year-by-year comparison
Balance at each anniversary under the three crediting paths.
| Year | Compounded yearly | Your schedule | Continuous | Compounding bonus |
|---|---|---|---|---|
| 0 | $10,000 | $10,000 | $10,000 | — |
| 1 | $10,600 | $10,617 | $10,618 | $17 |
| 2 | $11,236 | $11,272 | $11,275 | $36 |
| 3 | $11,910 | $11,967 | $11,972 | $57 |
| 4 | $12,625 | $12,705 | $12,712 | $80 |
| 5 | $13,382 | $13,489 | $13,499 | $106 |
| 6 | $14,185 | $14,320 | $14,333 | $135 |
| 7 | $15,036 | $15,204 | $15,220 | $167 |
| 8 | $15,938 | $16,141 | $16,161 | $203 |
| 9 | $16,895 | $17,137 | $17,160 | $242 |
| 10 | $17,908 | $18,194 | $18,221 | $285 |
How it's calculated
- Per period: 6.00% ÷ 12 = 0.5000%.
- Compound them: (1 + 0.5000%)^12 − 1 = 6.168% effective.
- On $10,000 that is $617 of first-year interest — $600 at the stated rate plus a $17 compounding bonus.
- Ceiling check: compounded continuously, the same 6.00% quote could yield at most 6.184%.
How to read these numbers
- On savings products the advertised APY already is the effective rate — two accounts with the same APY credit the same interest no matter how often they compound.
- Loan quotes are usually nominal: on your schedule a 6.00% quote really costs 6.168% a year, so compare loans on the effective figure.
- The nominal-to-effective gap grows with both the rate and the frequency — negligible in low single digits, but a 20% card rate compounded monthly is really 21.939%.
Know what this estimate is based on
- Jurisdiction
- General mathematical model
- Scope and limitations
- Projection only. Actual APY, posting dates, compounding, taxes, withdrawal rules, deposit protection, and fees depend on the financial institution and country.
- Source links checked
- Jul 30, 2026
Built and regression-tested by Smart Tools Lab. It has not been individually reviewed by a licensed financial, tax, or legal professional.
How to use
- 01
Pick a direction with the mode toggle: Nominal → effective turns a quoted rate into its true annual yield, while Effective → nominal recovers the required quote.
- 02
Type the annual rate in the rate field — either the nominal quote or your target effective rate — and watch the live conversion hint update as you type.
- 03
Select a compounding schedule from Annually through Daily, choose Continuous for the mathematical ceiling, or use Custom to enter any 1–365 periods per year, such as 26 for biweekly.
- 04
Optionally add a balance and a horizon of 1–50 years under Money illustration to see the conversion in dollars, or set the balance to 0 to compare rates alone.
- 05
Read the headline effective rate or required nominal, then scan the stats and the frequency table, where your selected schedule is badged and every alternative sits beside it.
- 06
Test the lever scenarios and the growth comparison chart to weigh rate changes against frequency changes, then print the page if you need a record of the conversion.
Formula
EAR = (1 + r/n)^n − 1 Continuous: EAR = e^r − 1 Periodic rate = r/n Reverse: r = n × ((1 + EAR)^(1/n) − 1) Reverse (continuous): r = ln(1 + EAR) r = nominal annual rate as a decimal · n = compounding periods per year · EAR = effective annual rate · e = Euler's number · ln = natural logarithm
Example
Suppose a bank quotes 6% and credits interest monthly. The calculator divides the quote by twelve to get a periodic rate of 0.5%, then compounds it across the year to an effective annual rate of 6.168% — an APY 0.168 percentage points, or 16.8 basis points, above the sticker figure. On a $10,000 balance, the stated rate alone would pay $600.00 in the first year, while monthly compounding actually delivers $616.78, a $16.78 bonus earned by interest landing on interest. Held for 10 years, the same quote grows the balance to $17,908.48 with annual crediting but $18,193.97 with monthly crediting, a $285.49 difference, while the continuous ceiling tops out at $18,221.19. Flip the mode and the closed-form reverse conversion shows the other direction: to earn an effective 6.17% with monthly crediting, a bank only needs to quote 6.002%, because compounding supplies the rest.
Definitions
- Nominal annual rate
- The quoted yearly rate before compounding is considered, formed by multiplying the periodic rate by the number of periods; it understates what a year of reinvested interest actually earns.
- Effective annual rate (EAR)
- The single once-a-year rate that produces the same result as the quoted rate under its compounding schedule; it is the honest basis for comparing offers with different schedules.
- Annual percentage yield (APY)
- The deposit-marketing name for the effective annual rate, required in US savings advertising by Regulation DD and published rounded to two decimals, which is why bank figures can differ slightly from exact math.
- Periodic rate
- The rate applied at each compounding interval — the annual quote split evenly across the year's periods; 0.5% per month on a 6% monthly quote.
- Compounding frequency
- How many times per year earned interest is added to principal and begins earning itself; more periods push the effective rate further above the nominal quote, with shrinking marginal gains.
- Crediting frequency
- How often a bank posts earned interest to your balance so you can see and withdraw it. Disclosures state compounding and crediting separately — model the stated compounding schedule; crediting only times the posting.
- Continuous compounding
- The limiting case of infinitely frequent compounding, computed as e^r − 1; it sets a strict ceiling that no calendar schedule reaches, though daily compounding lands very close to it.
- Basis point
- One hundredth of a percentage point, the standard unit for small rate differences; the gap between a 6% quote and its 6.168% monthly effective rate is 16.8 basis points.
- Rule of 72
- A mental shortcut for doubling time — 72 ÷ the rate in percent; at 6% compounded monthly it says 12.0 years against an exact 11.6.
- Regulation DD
- The Truth in Savings rule governing US deposit-account disclosures, which requires banks to advertise yield as APY rounded to two decimal places so savers can compare accounts consistently.
- Truth-in-Lending APR
- A loan-disclosure rate that folds certain fees and costs into the quote; unlike the pure nominal rate this calculator converts, it measures borrowing cost, not compounding arithmetic.
- Day-count convention
- The rule a bank uses to translate days into interest periods, commonly 360 or 365 per year; different conventions make published figures deviate slightly from textbook conversions.
Good to know
Two Honest Numbers Describe One Account
Every interest-bearing account carries two rates, and both of them are honest. The first is the nominal rate — the sticker number on the quote, such as 6%. It describes intent: the annual pace at which interest is supposed to accrue, stated before any compounding is taken into account. The second is the effective annual rate, and it describes outcome: the percentage by which a balance actually grows once a full year of crediting cycles has run. The two diverge because credited interest begins earning interest of its own. If a bank quotes 6% and credits monthly, each posting slightly enlarges the base on which the next month's interest is figured, and twelve rounds of that produce 6.168% of annual growth rather than 6.000%. Neither figure is a lie; the nominal rate is the input to the arithmetic, and the effective rate is its result. Trouble arrives only when someone treats one as the other — compounding a rate that has already been compounded, or lining up one institution's raw quote against another's realized yield as though they were the same species of number. That mismatch is the most common error in rate shopping, and eliminating it is this converter's entire job. Give it a quote and a crediting schedule and it reports the realized annual rate; give it a target yield and it reports the quote required to reach it. One boundary matters up front: the nominal rate here is a pure mathematical quote. It carries no fees, no taxes, no inflation adjustment, and no deposits or withdrawals — nothing but the relationship between a stated rate, a calendar of crediting events, and the yield those two facts jointly determine. Everything else on this page is built on that single, deliberately narrow conversion.
The Conversion Formula, Piece by Piece
The whole engine rests on one expression: effective rate = (1 + r/n)^n − 1. Each symbol earns its place. Start with r, the nominal annual quote written as a decimal, and n, the number of crediting events per year. Dividing r by n produces the periodic rate — the slice of interest actually applied at each event. At a 6% quote with monthly crediting, that slice is 0.5% per month, and the calculator displays periodic rates to four decimal places because tiny per-period differences matter once they are raised to a power. The expression (1 + r/n) turns the slice into a growth factor: multiplying a balance by 1.005 is the same operation as adding half a percent to it. The exponent n then applies that factor once per crediting event, and because multiplication stacks, each application works on the output of the one before. That stacking is compounding in its purest algebraic form — no cash flows, no fees, just repeated multiplication. After twelve rounds the combined factor is (1.005)^12, and subtracting 1 strips out the original principal to leave pure growth: 6.168%, or 6.167781% before the display rounds to three decimals. Notice what the formula guarantees. Because every crediting event builds on earlier credits, the effective rate can never fall below the nominal rate, and the two are equal only when n is 1, since a single annual posting has nothing earlier to compound. If r is zero, the expression collapses to zero for every schedule, which is why the calculator shows an empty state at 0% — there is nothing to convert when nothing accrues. The formula also explains why the gap widens as either r or n rises: more crediting events mean more stacking, and a larger quote makes every layer thicker.
A Field Guide to the Rate Acronyms
Four acronyms describe rates, and mixing them up costs money. APR, as this calculator uses the term, means the nominal annual quote — the raw stated rate before compounding is considered. APY, annual percentage yield, is the American deposit-marketing name for the effective annual rate; Regulation DD requires banks to publish it on deposit accounts so that savers can compare offers with the compounding already baked in. EAR, effective annual rate, is the same number wearing an analyst's badge — finance texts and spreadsheets prefer it. AER, annual equivalent rate, is the UK's regulatory label for the identical concept. Numerically, APY, EAR and AER are triplets; only their audiences differ. The trap sits inside APR. On the lending side, the Truth in Lending Act defines APR as a disclosure figure that folds origination fees, points and certain other charges into the rate, precisely so borrowers can see the all-in cost of credit expressed as a percentage. A mortgage APR is therefore not a pure nominal quote — it is a fee-loaded composite, and feeding it into this converter would answer a question nobody asked. This tool works exclusively with the mathematician's APR: a clean nominal rate with no fees, taxes or cash flows attached. When you type 6% here, you are asserting that interest accrues at a 6% annual pace and nothing else. Practical guidance follows directly. If a deposit account already shows an APY, that number is effective; run it through reverse mode if you want the underlying quote, but never through the forward direction, or you will compound the compounding. If a loan document shows a TILA APR, keep your expectations straight: this converter can handle its rate mathematics, but it cannot tell you what portion of that figure the fees contributed.
Climbing the Ladder From Annual to Daily
Hold the quote at 6% and vary only the calendar, and the effective rate climbs a ladder with unmistakably shrinking rungs. Annual crediting yields exactly 6.000% — one posting per year, nothing to compound. Semi-annual crediting lifts the yield to 6.090%. Quarterly reaches 6.136%, monthly 6.168%, weekly 6.180%, daily 6.183%, and continuous — the theoretical ceiling — 6.184%. Read the ladder twice. On the first pass, notice that every step up in frequency adds something; the engine enforces that the effective rate never falls as crediting events multiply. On the second pass, notice how quickly the additions collapse. The single move from annual to semi-annual crediting captures the largest gain anywhere on the ladder. By the time you pass monthly, the remaining rungs are nearly flat: weekly, daily and continuous crediting are separated by margins most account statements cannot even display. The pattern is the story. Each additional crediting event compounds a smaller slice of interest over a shorter stretch of the year, so the marginal payoff of frequency decays fast — diminishing returns in their cleanest mathematical form. This is why banks advertise daily compounding with such enthusiasm, and why the enthusiasm is largely cosmetic at deposit-account rates: the leap from annual to monthly genuinely matters, and almost everything past it is decoration. The calculator's frequency table lays the ladder out side by side, badges the schedule you selected, and draws a compounding-boost bar for each row so the shrinkage is visible at a glance. For calendars the preset buttons skip, the custom option accepts anything from 1 to 365 periods per year — 24 reproduces a semi-monthly cycle, 26 a biweekly one — and slots your schedule onto the same ladder so you can see exactly which rung your account occupies.
Continuous Compounding Without the Mystique
Push the crediting calendar past daily — hourly, every minute, every second — and the effective rate keeps rising, but toward a wall it can never cross. That wall is continuous compounding, computed as e^r − 1, where e is the mathematical constant that governs growth feeding on itself without pause. No real calendar sits behind it; it is the limit of (1 + r/n)^n − 1 as n grows without bound — the same limiting construction that defines e in the first place. At a 6% quote the ceiling sits at 6.184% — 6.183655% unrounded — and no schedule of discrete postings, not even one for every day of the year, quite touches it. What the mystique obscures is how little that last stretch is worth. Monthly crediting already turns a 6% quote into 6.168%, capturing a 16.8-basis-point compounding bonus; the continuous ceiling at 6.184% sits barely above that, and daily crediting at 6.183% closes almost all of the remaining distance by itself. The scenario cards make the triviality concrete: on $10,000 over ten years, switching the default monthly schedule to daily adds $26.32, while going all the way to continuous adds $27.22 — set the two gains side by side and the premium for infinite frequency over daily crediting all but disappears. So why include a continuous mode at all? Two reasons. Analytically, e^r − 1 is the standard convention in derivatives pricing and academic finance, so converting into and out of it is genuinely useful. Practically, the ceiling is a diagnostic: no advertised yield can exceed e^r − 1 for its stated quote under any crediting calendar whatsoever, which makes the continuous column a quick honesty check on marketing claims. Anything above the ceiling is not aggressive compounding; it is a different rate.
Reverse Mode: From Target Yield to Quote
Forward conversion answers what a quote delivers; reverse mode answers what a target demands. Flip the toggle to effective-to-nominal, enter the annual yield you want, choose a crediting schedule, and the calculator inverts the formula exactly: nominal = n × ((1 + EAR)^(1/n) − 1), or the natural logarithm ln(1 + EAR) when the schedule is continuous. No iteration or approximation is involved — the algebra runs backward as cleanly as it runs forward, so the recovered quote reproduces your target to the last displayed decimal. A worked anchor shows the shape of the result. To realize an effective 6.17% with monthly crediting, a bank need only quote 6.002%, applying a periodic rate of 0.500175% each month; twelve postings lift that modest quote the rest of the way to the target. Run the same 6.17% target across every schedule and the required quotes form a descending ladder: annual crediting demands the full 6.170%, semi-annual 6.078%, quarterly 6.032%, monthly 6.002%, weekly 5.991%, daily 5.988%, and continuous 5.987%. The lesson is the frequency story inverted: the more often an institution credits interest, the less it has to promise on the sticker to hand you the same realized yield, so a daily-crediting bank matches the 6.17% outcome while quoting just 5.988%. The same logic dissects published deposit offers. A 5% APY with daily crediting rests on a nominal rate of only 4.879% — the number actually applied each day is meaningfully smaller than the number in the advertisement, with compounding supplying the difference. Reverse mode is therefore the negotiating half of the pair: it translates the yield you want into the quote you should be looking for, under whatever crediting calendar the institution actually uses. The custom schedule works here as well: if your account posts interest on a biweekly or semi-monthly cycle, reverse mode returns the exact quote that particular calendar requires instead of an approximation borrowed from the nearest preset.
When Frequency Matters and When It Doesn't
The lever scenarios exist to settle a recurring argument: should you chase a better rate or better compounding? Start from the default — $10,000 at a 6% quote, credited monthly, left alone for ten years — and pull each lever separately. Raising the quote by a single point to 7%, which is effectively 7.229% with monthly crediting, ends the decade at $20,096.61, a gain of $1,902.65 over the base case. Keeping the 6% quote but upgrading from monthly to daily crediting ends at $18,220.29, a gain of $26.32. Going all the way to the continuous limit adds $27.22. One percentage point on the sticker outweighs the entire frequency spectrum by a factor in the dozens, so hunting a higher quote is nearly always worth more of your attention than hunting a busier calendar. There is, however, a regime where frequency stops being a rounding error, and it lives on the borrowing side. The gap between nominal and effective grows with the level of the rate, not just the count of crediting events. At 6%, monthly compounding adds 0.168 percentage points to the quote. At a 20% card-style rate compounded monthly — a periodic rate of 1.6667% per cycle — the effective rate is 21.939%, a gap of nearly two full points between the number quoted and the number experienced. On a $5,000 revolving balance, a year of that compounding produces $1,096.96 of interest against the $1,000.00 the stated rate implies. The practical rule falls out cleanly: for deposit accounts at ordinary rates, compare quotes first and treat frequency as a tiebreaker; for high-rate debt, always convert to the effective rate before judging the cost, because the sticker understates it by a margin that genuinely moves a budget.
Reading a Bank Disclosure Like an Analyst
A deposit disclosure rewards a close reading, and the effective-rate lens is the right pair of glasses. First rule: an APY is already an effective rate. Regulation DD obliges banks to compute the compounding into that figure before publishing it, so running an advertised APY through the forward direction of this converter double-counts the compounding and produces a yield no account will ever pay. If you want the machinery underneath an APY, use reverse mode with the bank's actual crediting schedule. Second rule: published APYs are rounded to two decimal places under Regulation DD, while this calculator carries annual rates to three decimals and periodic rates to four, so an exact conversion can sit a hair away from the printed figure without either number being wrong. A 5% quote compounded daily converts to 5.127% effective — worth $512.67 of first-year interest on $10,000 — and the bank's advertisement will show a two-decimal rounding of that yield. Third rule: separate the compounding language from the crediting language. A typical disclosure says interest is compounded daily and credited monthly — model that account as Daily, because accrued interest starts earning on itself immediately even though it only appears in the balance at month-end. Crediting decides when earnings become visible and withdrawable; the stated compounding schedule decides how they stack. The rare agreement that compounds only when interest posts should be modeled on its posting schedule instead. Fourth rule: check the day-count basis. Some banks divide the year into 360 days for accrual purposes while others use 365, and the two conventions produce slightly different published yields from identical quotes. Finally, treat promotional teaser rates as a different instrument altogether: a rate guaranteed for three months is not an annual rate at all, and converting it as though it will persist for a year manufactures yield the fine print has already taken away. None of these wrinkles break the mathematics; they only decide which numbers deserve to enter it.
Doubling Time and Other Mental Math
The effective rate unlocks a small family of quick calculations, and doubling time is the most satisfying of them. The exact answer is ln 2 divided by ln(1 + EAR): at a 6% quote credited monthly — 6.168% effective — money doubles in 11.6 years. The famous Rule of 72 approximates the same answer by dividing 72 by the rate, giving 12.0 years, and the calculator shows both figures side by side so you can watch the shortcut's error in real time. Here the rule runs long by a few months — respectable accuracy for arithmetic you can do at a stoplight. The rule's precision is not uniform, though. It is tuned for mid-single-digit rates compounded about once a year; push toward high double-digit rates or toward continuous crediting and the drift widens, consistently overstating how long doubling takes when compounding is frequent. Whenever the stakes are real, let the exact logarithm — which the tool computes from the effective rate, never from the nominal one — settle the question. The second piece of mental math is vocabulary: basis points. One basis point equals a hundredth of a percentage point, and small compounding gaps live at precisely that scale. Saying that monthly crediting turns a 6% quote into 6.168% sounds negligible; saying the same account collects a 16.8-basis-point compounding bonus — the tool reports the gap both ways — gives the difference a unit that professionals can price. Institutional desks argue over single basis points because at scale they are real money, and adopting the unit does the same work for your own comparisons: it stops small-looking decimals from being waved away, and it stops marketing from dressing up trivial frequency gains as meaningful yield. One caution ties the two ideas together: exact doubling time is an effective-rate calculation, while the Rule of 72 remains a quote-based shortcut — which is precisely why it drifts. Keep each number tied to its proper baseline and neither piece of mental math will mislead you.
The Default Example, End to End
Everything the calculator does can be watched in one run. Enter a 6% nominal quote, choose monthly crediting, and set the money illustration to $10,000 over a ten-year horizon. The headline reports 6.168% effective — 6.167781% at full precision — built from a 0.5% periodic rate, and the stat strip shows the 0.168-percentage-point gap, its 16.8-basis-point translation, and the 6.184% continuous ceiling overhead. The donut splits the first year's interest into its two ingredients: $600.00 that the stated rate alone would have produced, plus a $16.78 compounding bonus, for $616.78 in total. The growth comparison then stretches the same quote across a decade under three crediting paths. Compounded once a year, the balance reaches $17,908.48. Credited monthly, it reaches $18,193.97 — and the $285.49 spread between those two figures is the ten-year price of ignoring compounding frequency at this rate. The continuous path tops out at $18,221.19, barely above the monthly line, confirming on a chart what the frequency ladder showed in percentages. The year-by-year table beneath the chart lets you watch the three paths separate: identical at the start, a few dollars apart in the early years, then steadily diverging as each year's credited interest joins the base for the next. To adapt the run, replace the quote with your bank's stated rate, pick the schedule that matches the disclosure's crediting language, and set the balance and horizon to your own situation — or set the balance to zero to strip the dollars away and compare pure rates. Nothing in the run involves fees, taxes, deposits or withdrawals — the illustration isolates the rate conversion itself, which is exactly what keeps the comparison honest. Then flip to reverse mode and ask the opposite question of the same setup: what quote would a bank need to post, under its own calendar, to hand you the effective yield this example produced.
Frequently asked questions
What is an effective annual rate?
The effective annual rate (EAR) is what a quoted interest rate truly delivers over a full year once compounding is folded in. A bank can advertise 6% compounded monthly, but once every monthly credit begins earning on its own, the year's true yield is 6.168%. The nominal quote describes the raw rate; the effective rate describes the outcome. Whenever two offers compound on different schedules, their nominal quotes are not directly comparable — converting both to effective annual terms puts them on the same footing, which is exactly the conversion this calculator performs.
What's the difference between EAR, APY, and APR?
APY and EAR are the same number wearing different labels, while an APR-style nominal quote is the raw rate before compounding. APY (annual percentage yield) is the name US deposit marketing must use under Regulation DD; EAR — or AER in the UK — is the same figure in analyst language. The nominal rate, often loosely called APR, is simply the per-period rate scaled to a year with no compounding counted. In this calculator the nominal input is a pure quote; it is not the fee-loaded APR that appears on loan disclosures. Convert nominal to effective and you have the APY.
How do I convert an APR to an APY?
Divide the nominal quote by the number of compounding periods, then compound that periodic rate through a full year: APY = (1 + r/n)^n − 1. Take 6% compounded monthly: the periodic rate is 0.5% per month, and twelve of those steps stack up to an APY of 6.168% (6.167781% before display rounding). The lift over the stated quote is 0.168 percentage points, or 16.8 basis points. In this tool you simply enter the nominal rate and pick the schedule, and the effective figure appears in the headline — the step-by-step explainer walks the same arithmetic.
How do I work backwards from a target APY to the nominal rate?
Switch the mode toggle to "Effective → nominal" and the calculator inverts the formula exactly: nominal = n·((1 + EAR)^(1/n) − 1), or ln(1 + EAR) for continuous compounding. To end up with an effective 6.17% under monthly crediting, the quote must be 6.002%, which works out to a periodic rate of 0.500175% per month. Because more frequent schedules do more of the lifting, the required quote falls as frequency rises: 6.170% annually, 6.078% semi-annually, 6.032% quarterly, 6.002% monthly, 5.991% weekly, 5.988% daily, and 5.987% continuous. It is a closed-form calculation, not an approximation.
What is continuous compounding?
Continuous compounding is the mathematical limit where interest is credited at every instant, and its effective rate is e^r − 1, where e is Euler's number. At a 6% quote the continuous ceiling is 6.184% (6.183655%) — only a hair above daily compounding's 6.183%. No calendar schedule ever reaches the ceiling; it is a strict upper bound, and no US bank actually credits interest continuously. The figure is still useful: it tells you the absolute most a given quote can yield, so if daily compounding already sits within a fraction of a basis point of it, shopping for finer schedules is pointless.
Does compounding frequency really matter?
Far less than the rate itself, and the scenario panel proves it in dollars. Starting from the default — $10,000 at a 6% quote compounded monthly for 10 years — switching to daily compounding adds just $26.32 to the ending balance, and even the continuous ceiling adds only $27.22. Raising the quote a single point to 7% (an EAR of 7.229%) ends at $20,096.61, a gain of $1,902.65 that dwarfs the daily-compounding bump. Frequency is worth checking when two offers are otherwise identical, but when they differ, negotiate the quote first and treat the schedule as a tiebreaker.
Why doesn't my bank's published APY match this calculator exactly?
Small mismatches usually trace to rounding and day-count rules rather than errors. Regulation DD lets banks publish APY rounded to two decimal places, while this calculator carries three, so 6.168% may appear as 6.17% on a rate sheet. Banks also compute daily interest under 360-day or 365-day conventions, which nudges the annualized figure slightly, and some accounts net out maintenance fees or tiered balances that a pure rate conversion ignores. If a published APY differs from this tool by more than a couple of basis points, look for a fee, a tier, or a promotional period rather than a math problem.
Is the APR in this calculator the same as the APR on a loan disclosure?
No — they share a name but not a definition. The APR printed on a mortgage or auto-loan disclosure is governed by the Truth in Lending Act and folds origination charges, points, and certain fees into a single legally defined figure, which is why it usually sits above the note rate. The nominal rate this converter works with is a pure quote: the bare annual rate before any compounding, with nothing else baked in. Comparing a TILA APR from a loan estimate against an effective rate from this tool would mix two different measurements. Use this tool for rate-to-rate conversions only.
What compounding schedule do savings accounts actually use?
Check the deposit agreement's exact wording: most US savings accounts state that interest is compounded daily and credited monthly. The compounding language is the one to model — an account that compounds daily belongs on the Daily setting even though the money only appears in your balance once a month, because accrued interest starts earning on itself from the day it accrues. Crediting timing decides when earnings become visible and withdrawable, not how they stack. Only if an agreement says interest compounds when posted should you match the posting schedule instead — Monthly for a month-end poster.
What is the periodic rate and when is it useful?
The periodic rate is the nominal quote divided by the number of compounding periods — the slice of interest actually applied each period, shown here to four decimals. It matters most on revolving debt: a 20% card-style rate compounded monthly means 1.6667% is charged each month, and those twelve charges stack to an effective 21.939%. On a $5,000 balance carried for a year, that is $1,096.96 of interest versus the $1,000.00 the stated rate implies. Statements and billing math run on the periodic rate, so seeing it explicitly helps you check a statement line or reconstruct a month's charge.
How does the time-to-double figure work?
The calculator reports two doubling estimates: the exact answer, computed from the effective rate, and the classic Rule of 72 shortcut, which divides 72 by the quoted rate. At 6% compounded monthly, money doubles in 11.6 years exactly, while the Rule of 72 estimates 12.0 — close enough for a mental check, a few months off in practice. The gap exists because the rule ignores compounding frequency and is calibrated for mid-single-digit rates. Showing both side by side lets you use the shortcut in conversation while trusting the exact figure for planning.
Can the effective rate ever be lower than the nominal rate?
Not in this calculator, and not under ordinary compounding math. For every schedule of one or more periods per year, the effective rate is at least the nominal rate, and the two are equal only under annual compounding, where there is nothing within the year to compound. The gap widens as either the rate or the frequency rises. At 0% every schedule yields exactly 0%, so the empty state simply notes that nominal and effective coincide at zero. The tool does not accept negative rates, so the below-nominal territory that negative-rate math could create never arises here.
What is the Custom compounding frequency for?
Custom lets you enter any whole number of compounding periods from 1 to 365 a year, covering schedules the preset buttons skip. Enter 24 for semi-monthly crediting — interest posted twice a month — or 26 for biweekly, the payroll-style calendar some credit unions and employer-linked accounts follow. It also handles oddities like bimonthly crediting, entered as 6 periods per year. Because the conversion formula only needs the period count, any calendar you can describe as n equal steps per year works. The frequency table updates to show how your custom schedule ranks against the standard ones.
What does this calculator leave out?
Fees, taxes, inflation, and cash flows — it is deliberately a pure rate converter. It answers one question, in both directions: what a nominal quote is worth as an effective annual rate under a given schedule, and what quote a target effective rate requires. The optional money illustration projects a single untouched balance only to translate a rate gap into dollars; it does not model deposits, withdrawals, maintenance charges, or the tax owed on interest. If you need those layers — recurring contributions, fee drag, after-tax growth — use a dedicated savings or planning tool and bring the effective rate from here as its input.