APR vs APY Calculator
Savings & BankingHow compounding turns APR into APY.
Rate & compounding
Money illustration
Conversions use exact compound arithmetic; rates display to three decimals and periodic rates to four. The APR here is the plain nominal rate — not a fee-loaded loan APR. No fees, taxes or inflation are modeled.
The same rate, two sides of the ledger
On $10,000 over 5 years, compounding moves $334 — into your pocket as a saver, out of it as a borrower.
A 5.00% APR deposit really earns at 5.116% APY, so it pays $334 more than the $2,500 a flat rate would — compounding works for you.
A 5.00% APR balance left to compound really costs at 5.116% APY, $334 above the $2,500 the sticker rate implies — compounding works against you.
Assumes a revolving balance that compounds and is not paid down. Installment loans (auto, mortgage) amortize and use the disclosed loan APR instead.
- At the flat rate$2,500
- Added by compounding$334
Total interest over the horizon, split into what the flat rate alone would pay and the extra that compounding stacks on top.
What the rate really does over time
$10,000 at both readings of the rate, tracked year by year over 5 years.
Year-by-year: flat rate vs compounding
Interest to date at the sticker APR, at the real APY, and the gap between them.
| Year | At the flat rate | With compounding | Gap |
|---|---|---|---|
| 0 | $0 | $0 | — |
| 1 | $500 | $512 | $12 |
| 2 | $1,000 | $1,049 | $49 |
| 3 | $1,500 | $1,615 | $115 |
| 4 | $2,000 | $2,209 | $209 |
| 5 | $2,500 | $2,834 | $334 |
How the gap changes with compounding
The same 5.00% APR, read as an APY under a few schedules — denser compounding widens the gap.
| Frequency | APR | APY | Gap (bps) | Year-1 gap |
|---|---|---|---|---|
| Annually | 5.000% | 5.000% | 0.0 | $0 |
| MonthlySelected | 5.000% | 5.116% | 11.6 | $12 |
| Daily | 5.000% | 5.127% | 12.7 | $13 |
| Continuous | 5.000% | 5.127% | 12.7 | $13 |
How it's calculated
- Split the APR across the periods: 5.00% ÷ 12 = 0.4167% per period.
- Compound every period: (1 + 0.4167%)^12 − 1 = 5.116% APY.
- The APR-to-APY gap is 0.116 percentage points — 11.6 basis points.
- On $10,000, year one earns $512 instead of the $500 a flat rate implies — a $12 difference that compounds to $334 over 5 years.
How to read these numbers
- APR (annual percentage rate) is the plain nominal quote — the periodic rate scaled up to a year, before any compounding is counted.
- APY (annual percentage yield) is the effective rate once each period's interest starts earning too; it is at least the APR, and higher whenever interest compounds more than once a year.
- Institutions tend to advertise whichever number flatters them — the larger APY on savings they pay you, the smaller APR on loans you pay them. Convert to compare like with like.
- This APR is pure compounding math. A loan disclosure's APR also folds in fees and points, so it is not the same figure — reach for a loan APR tool for that.
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 your direction with the mode toggle: choose APR to APY when you know the nominal rate a lender or bank quotes, or APY to APR when you know the effective yield and want the underlying nominal rate behind it.
- 02
Type the known rate into the rate field. In APR-to-APY mode enter the nominal APR you were quoted; in APY-to-APR mode enter the effective APY. Use up to three decimals for precision.
- 03
Choose a compounding schedule: annual, semiannual, quarterly, monthly, weekly, or daily. Pick Continuous for the mathematical ceiling, or Custom to key in your own number of periods per year for an unusual quote.
- 04
Optionally enter a deposit or carried balance and a time period in years. This turns the abstract rate gap into real dollars on both sides and unlocks the impact chart and the year-by-year table below.
- 05
Read the headline converted rate at the top, then scan the APR-vs-APY compare panel: it shows the periodic rate, the spread in percentage points and basis points, and how the same nominal rate shifts across every schedule.
- 06
Explore the two-sided earn-versus-pay panels to see a saver's bonus and a borrower's hidden cost side by side, then study the flat-versus-compounded impact chart and the year-by-year table to watch the gap widen.
Formula
APY = (1 + APR/n)^n - 1 Continuous: APY = e^APR - 1 Reverse APR = n * ((1 + APY)^(1/n) - 1) Continuous reverse: APR = ln(1 + APY) Periodic rate = APR / n Spread = APY - APR (x100 = basis points) Where: APR = nominal annual rate; APY = effective annual yield; n = compounding periods per year; e = Euler's number (~2.71828); ln = natural logarithm
Example
Start with the tool's defaults: a 5% APR compounded monthly on 10,000 dollars over 5 years. Twelve periods a year turn a 0.417% periodic rate (0.4167%) into an APY of 5.116% (5.116190%), a spread of 0.116 percentage points, or 11.6 basis points. In year one that spread is exactly the dollar gap: simple interest at the flat 5% pays 500.00, while monthly compounding delivers 511.62, a difference of 11.62 that is precisely 10,000 times the spread. Over the full 5 years the gap widens past that, because compounding stacks on compounding: the flat sticker figure totals 2,500.00 in interest, but the real compounded interest is 2,833.59, a 333.59 gap. Ending balances land at 12,500.00 flat versus 12,833.59 compounded. Read from the saver's side, that 333.59 is a bonus you earn beyond the headline rate. Flip to the borrower's side and the same 333.59 is a hidden cost the APR label never shows on a carried, revolving balance. One rate, two wallets. Now switch to APY-to-APR mode and enter a target APY of 5.000% with monthly compounding: the tool reports that you need a nominal APR of only 4.889% (4.888949%) to reach it, since compounding quietly does the rest.
Definitions
- APR (nominal)
- The stated yearly rate before compounding is counted. Split it across the year's compounding periods to get the rate charged or paid each one. Lenders lead with it because it reads smaller than the yield the same rate actually produces.
- APY
- The true yearly rate after compounding is folded in, so it already reflects interest earning interest. Banks quote it on deposits because, for any rate above zero compounded more than once a year, it reads higher than the matching APR.
- APR-to-APY spread
- The gap between the two labels, APY minus APR, stated in percentage points or basis points. It is zero under annual compounding and widens as frequency rises. On a $10,000 deposit at 5% monthly it is 0.116 points.
- periodic rate
- The APR sliced into equal pieces, one for each compounding step: the actual rate applied every period. At 5% APR compounded monthly it is 0.417% per month; a card at 22% APR applies 1.833% every month.
- compounding frequency
- How many times a year interest is figured and added to the balance: annual, semiannual, quarterly, monthly, weekly, daily, or continuous. More frequent compounding raises the APY a given APR produces; annual compounding leaves the APY equal to the APR.
- continuous compounding
- The limiting case where interest is added every instant, so APY = e^APR − 1. It sets the highest yield any APR can reach; at 5% APR it produces a 5.127% APY, barely above daily compounding.
- simple (flat) interest
- Interest figured only on the original amount, amount times rate times years, with nothing earned on prior interest. It is the sticker mental-math figure; the real compounded number is at least as large and usually larger over multiple years.
- revolving balance
- A balance that is carried and not paid down, such as an unpaid credit-card or line-of-credit balance, so interest keeps compounding on it. This tool's borrower cost assumes exactly this; it does not describe an amortizing loan being paid off.
- nominal vs fee-loaded (TILA) APR
- This tool uses the plain nominal APR, pure compounding math with no costs added. A loan's disclosed APR under Truth in Lending bakes in points and fees, so it runs higher than the nominal rate and is not interchangeable with it.
- basis point
- One hundredth of a percentage point; 100 basis points equal 1%. Rate gaps are often quoted this way for precision. The 0.116-point spread on the default deposit is 11.6 basis points; a 22% card's spread is 236.
- effective yield
- Another name for the APY: the rate you actually earn or pay once compounding is included. Comparing the effective yield of two offers, rather than their stated APRs, is the only apples-to-apples way to rank them.
Good to know
Two Labels for One Rate - and Who Picks Which
Every compounding rate has two legal names, and the one you see depends on who is doing the quoting and which number flatters them. A lender advertising a loan or card shows you the APR - the annual percentage rate, the plain nominal figure before compounding is folded in. A bank advertising a deposit shows you the APY - the annual percentage yield, the same rate after compounding is folded in. The underlying math is identical; only the label changes, and the label is chosen to make the offer look better. That choice is not neutral, and it always runs the same direction. Compounding makes APY at least as large as APR, equal only when interest posts once a year. So a saver is shown the bigger of the two numbers (APY, because a higher yield sells a deposit), while a borrower is shown the smaller one (APR, because a lower rate sells a loan). The institution keeps the flattering label and quietly leaves you to work out the other side. Take the tool's default: 5% APR compounded monthly is a 5.116% APY. A bank would headline "5.116%"; a card issuer at the same underlying rate would headline "5%." Same periodic rate of 0.417% a month, opposite marketing. This tool exists to put both labels in front of you at once, so you are never comparing a yield you earn against a rate you pay without converting first. When you deposit, you want to know the APY, because that is what actually lands in your account. When you borrow and carry a balance, you want to know the APY-equivalent of the quoted APR, because that is what the debt actually costs. Knowing which label the institution picked - and why - is the first move in reading any offer honestly.
One Formula, and Why the First-Year Gap Is Just the Spread
One equation drives everything here. Split the APR into n equal periods, earn the periodic rate APR/n each period, and let it compound: APY = (1 + APR/n)^n - 1. At the default 5% APR over twelve monthly periods the periodic rate is 0.417%, and stacking those twelve periods gives an APY of 5.116%. The spread - APY minus APR - is 0.116 percentage points, or 11.6 basis points. That spread has a clean dollar meaning in the first year, and only the first year. Over one year, simple interest on a balance is amount x APR, and compound interest is amount x APY. Subtract them and the APR term cancels, leaving amount x (APY - APR) - the balance times the spread, exactly. On 10,000 dollars the year-one gap is 10,000 x 0.116%, which is 11.62 dollars: the difference between 500.00 of flat interest and 511.62 of compounded interest. No approximation, no rounding trick - the first-year gap is simply the spread expressed in dollars. People often assume that gap holds steady, that each year adds another 11.62 dollars. It does not, and this is the point most sticker estimates miss. After year one, compounding starts working on interest that itself already compounded, so the gap widens faster than the spread alone predicts. Over the default five years the flat calculation gives 2,500.00 of interest while the compounded balance earns 2,833.59 - a gap of 333.59, far more than five times 11.62. The ending balances tell the same story: 12,500.00 flat against 12,833.59 compounded. So the spread is exact only as a one-year snapshot. Read it that way and it is a precise, trustworthy number. Project it in a straight line across many years and you will understate what compounding actually does - in your favor when you save, against you when you carry a balance.
Sticker Math vs Real Math: What You Assume vs What You Get
Most people size up interest with sticker math: multiply the balance by the rate by the number of years. It is fast, it uses the APR the lender or bank first says out loud, and it is what your head reaches for. The tool labels this the flat figure - amount x APR x years - and shows it beside the real figure, amount x (1 + APY)^years, so you can see exactly how far the shortcut drifts. At the default the two start close and separate steadily. Sticker math on 10,000 dollars at 5% for five years says 2,500.00 of interest and a 12,500.00 ending balance. The real, monthly-compounded path earns 2,833.59 and ends at 12,833.59. The shortcut is off by 333.59 - about 13% of the interest it was trying to estimate - and every extra year widens the miss because the flat line grows straight while the real one curves upward. Which direction that error hurts depends on which side of the deal you are on. When you save, sticker math undersells you: you will actually earn more than the flat figure, so the shortcut makes a good account look worse than it is. When you borrow and let a balance ride, sticker math flatters the debt: you will actually owe more than the flat figure, so the shortcut hides part of the cost. In both cases the honest number is the compounded one, and it is always the larger. The takeaway is not that simple interest is wrong arithmetic - it is a real quantity, the flat line the tool draws. The takeaway is that almost nothing you hold pays or charges simple interest. Deposits and carried balances compound, so the flat figure is a floor, not an estimate. Use it as a quick sanity check, then trust the compounded number for any decision that turns on the actual dollars.
Reading a Savings Offer: They Quote You the APY
When you shop for a deposit - savings account, money market, CD - the headline number is almost always the APY, and that works in your favor. The APY already has compounding baked in, so it is the true annual return on your money. Two accounts quoted as APYs can be compared straight across: the higher APY earns more over a year on the same balance, full stop, with no conversion needed. The number the APY represents is what actually lands in your account. Park 10,000 dollars at a 5.116% APY and after one year you have earned 511.62 dollars - not the 500.00 that the underlying 5% nominal rate might suggest. That extra 11.62 is the compounding the bank has already credited into the headline figure. Over five years the same account grows to 12,833.59, and every dollar of that 2,833.59 gain is money the APY promised up front. The catch is when a bank quotes something other than APY. Some offers lead with a nominal "interest rate" or "rate" and mention the APY only in the fine print, or state a rate and a compounding frequency and leave you to finish the arithmetic. That is your cue to convert up before comparing. A 5% rate compounded monthly is a 5.116% APY; the same 5% compounded daily is a 5.127% APY. Line those APYs up against a competitor's headline APY - never a nominal rate against a yield, or you will hand the comparison to whichever bank quoted the flattering label. One honest limit: this tool models the rate math only. It assumes no fees, no minimum-balance penalties, no taxes on the interest, and a rate that holds steady. Real accounts can carry monthly fees or promotional rates that expire, and interest is usually taxable. Treat the APY as the ceiling the rate alone can deliver, then check the account's other terms before you commit.
Reading a Card or Credit Offer: They Quote You the APR
Borrowing flips the label. A credit card or line of credit leads with the APR, the nominal rate, because it is the smaller of the two numbers and a lower rate sells debt. But if you carry a balance that compounds instead of paying it off, the APR understates what you actually owe. To see the real cost you have to convert the APR up to its APY, exactly the move a saver makes - just now it is working against you. Take a card at 22% APR compounded monthly. Converted, that is a 24.360% APY - a spread of 2.360 percentage points, or 236 basis points, that the APR label never shows. On a 6,000 dollar balance carried for a year, sticker math on the 22% says 1,320.00 of interest. The real compounded cost is 1,461.58. The 141.58 difference is money the APR quietly left out of the headline. A line of credit tells the same story at a gentler rate and a faster clock. At 9.5% APR compounded daily, the APY is 9.965% - a 0.465-point, 46.5-basis-point spread. Carry 8,000 dollars for three years and the flat estimate is 2,280.00, while the compounded cost is 2,637.70, a gap of 357.70. Daily compounding on a borrowed balance works precisely as hard as it does on a deposit, only you are on the paying end. Two limits matter here. First, this figure assumes a revolving, non-amortizing balance - one that sits and compounds, not one you pay down on a schedule. An installment loan that amortizes behaves differently and is quoted under its own disclosed APR. Second, the tool models pure rate math with no fees, late charges, or taxes. So read the compounded APY as the cost of the rate alone on a carried balance, then treat any fees the lender adds as cost stacked on top.
Comparing Two Offers Quoted in Different Units
When one institution hands you an APR and another hands you an APY, you are not looking at the same number in two outfits. You are looking at two different measurements, and lining them up side by side tells you nothing until you convert both to one unit. Pick the unit that matches your side of the deal. If you are the saver, restate everything as APY, because APY is what actually lands in your account. If you are the borrower, look at the periodic rate and the compounding schedule, because that is what actually accrues on your balance. Take two savings offers. Bank A advertises "5.000% APY, compounded monthly." Bank B advertises "5% APR, compounded monthly." At a glance B looks like the loser, just a plain rate with no APY on it, but run B through the formula and its APY is 5.116%. On a 10,000 dollar deposit that is 511.62 versus 500.00 in the first year, a 11.62 dollar edge to the offer that looked plainer. A nominal rate quoted with frequent compounding can quietly beat a headline APY that happens to be lower. Now flip it. To actually deliver a 5.000% APY with monthly compounding, a bank only needs to post a 4.889% nominal APR. So a "5% APR, monthly" offer and a "5.000% APY" offer are not a tie: the first wins, because 5% nominal compounds up to 5.116%, well past 5.000%. The rule that survives every version of this: never compare an APR to an APY directly. Convert first. If both are quoted the same way and compound the same way, the bigger number wins. If the units differ, enter each offer into the tool, read both its APR and its APY, and compare them in whichever unit governs your wallet.
How Compounding Frequency Widens the Gap
Hold the nominal rate fixed at 5% and change only how often it compounds, and you watch the gap between APR and APY open from nothing to its ceiling. Compounded once a year, the APY is exactly 5.000%, and there is no gap at all, because no intra-year interest is earning its own interest. Move to monthly and the APY climbs to 5.116%, a spread of 11.6 basis points. Move to daily and it reaches 5.127%, about a 12.67 dollar first-year difference on a 10,000 dollar balance. Push to continuous compounding and you hit 5.127% as well, the mathematical ceiling, the most any 5% nominal rate can ever become. Notice how the returns diminish. Going from annual to monthly buys you most of the spread. Going from monthly to daily adds barely a basis point. Going from daily to continuous adds almost nothing you can measure in cents. Frequency matters, but it saturates fast, and the first jump, away from annual, is the one that moves real money. This is a lever the institution controls, and which way it helps depends on your side. As a saver you want compounding as frequent as possible, because every extra period is interest working for you, so the daily-compounded account quietly beats the annual one at the same posted rate. As a borrower on a revolving balance you want the opposite, and you rarely get it: cards compound monthly or daily, and each period stacks charges on charges you have not paid. When you read an offer, the compounding schedule is not fine print to skim past. It is the difference between 5.000% and 5.127% on the same 5% headline. The gap-by-frequency strip in the tool lays all the schedules next to each other so you can see exactly what the choice of period is worth on your own amount.
When the Gap Is Big Enough to Change Your Decision
Not every gap deserves your attention. The question is not whether APR and APY differ, because they always do above 0% with more-than-annual compounding, but whether the difference is large enough to change what you do. Two things drive its size: the rate and the balance. Both have to be big before the spread earns a decision. At the default 5% monthly, the spread is 11.6 basis points and the first-year gap on 10,000 dollars is 11.62 dollars. That is real, but it will rarely flip your choice between two comparable savings accounts. Chase it if the offers are otherwise identical, ignore it if one account has better terms elsewhere. Small rate, small spread, small stakes. Now raise the rate. A credit card at 22% APR compounded monthly carries a 24.360% APY, a spread of 2.360 percentage points, or 236 basis points, twenty times the savings gap. On a 6,000 dollar balance carried for a year, the real cost is 1,461.58 while the sticker "22% times 6,000" math says 1,320.00. The APR label hides 141.58 dollars. That number is big enough to change behavior: it is the difference between "I'll carry this a while" and "I'll pay it down first." The pattern is that trouble compounds when a high rate and a large revolving balance sit together over time. A 9.5% line of credit at 8,000 dollars over three years hides 357.70 dollars behind its 9.5% APR versus a true 9.965% APY. Neither the rate nor the balance alone is alarming; together they add up. Use a simple filter. On the earning side, a spread under about 15 basis points is a tiebreaker, not a reason on its own. On the paying side, treat any revolving balance above a few thousand dollars at a double-digit rate as a spread worth acting on.
This APR Is Not the APR on a Loan Disclosure
There are two things called "APR," and this tool uses only one of them. Here the APR is the plain nominal rate: pure compounding math, the periodic rate times the number of periods, nothing else baked in. On a mortgage, auto loan, or personal loan, the APR printed on your Truth in Lending disclosure is a different animal. It folds origination points, fees, and certain closing costs into a single rate so you can compare the all-in cost of borrowing. That disclosed APR is deliberately higher than the note's stated interest rate, and you cannot reconstruct it from the (1 + APR/n)^n formula, because fees are not compounding; they are added on. So do not take a number from this tool and treat it as a loan's disclosure APR, and do not take a disclosure APR and expect its APY here to say anything about your loan's cost. They answer different questions. The disclosure APR answers "what does this loan cost me all in, as a yearly rate?" This tool answers "what does this nominal rate actually compound to?" The second boundary matters just as much. Every borrower figure here assumes a revolving, non-amortizing balance: a carried credit-card balance or a drawn line of credit that sits there compounding and never gets paid down. Installment loans do the opposite. An auto loan or mortgage amortizes, so each payment retires part of the principal and the balance the interest applies to shrinks every month. The compounded-balance cost this tool shows would badly overstate what you actually pay on an amortizing loan, because you never let the full balance ride. Use this tool for what it is built for: converting a plain rate between its APR and APY forms, and pricing interest on a balance that compounds untouched. For the true cost of a loan you make payments on, read the amortization schedule and the disclosure APR instead.
The Default Example, Both Sides, End to End
The tool draws the default - 5% APR, monthly, 10,000 dollars, five years - as one APY of 5.116% and two pictures, and the pictures are where reading replaces arithmetic. The conversion and the dollar identities are laid out in full in the example block above: 500.00 flat against 511.62 compounded in year one, 2,500.00 against 2,833.59 over five years. What the two-line chart and the year-by-year table add is a way to watch those numbers move rather than just land. Start with the chart. The flat line is straight because sticker interest adds the same amount every year - one constant slope from the origin, no bend. The compounded line leaves it at exactly the year-one gap and then curves upward, pulling away a little more each year. At any year, the height separating the two lines is that year's gap, and the fact that this distance grows - rather than holding fixed at the year-one figure - is compounding stacking on itself, drawn to scale. By year five the visible gap is the 333.59, plainly wider than five year-one steps stacked flat. The year-by-year table makes the same thing countable. Read down the two interest columns and the gap in each row widens; read the ending-balance columns and the compounded balance pulls ahead row by row until it reaches 12,833.59 against the flat 12,500.00. Then read that single 5.116% APY from both sides of your wallet. As a saver, the upward curve and the 12,833.59 ending balance are money working for you - the compounded side is the one you keep. As a borrower carrying that 10,000 dollars on a revolving balance, the identical upward curve is cost accruing against you, and the same 333.59 is interest the "5% APR" label never advertised. One APY, one chart, opposite meaning depending on which side of it you sit - which is the entire point of the tool.
Frequently asked questions
APR vs APY: what's the real difference?
The two are one interest rate seen from opposite sides. APR is the nominal rate before compounding — spread it over the year's periods to get each period's rate. APY is what that rate actually produces once interest starts earning interest. At 5% APR compounded monthly the APY is 5.116%, a spread of 0.116 percentage points. Lenders tend to quote the smaller APR, banks the larger APY, but the underlying math is identical; only the label, and which side of your wallet it sits on, differs.
How do I convert APR to APY and back?
To go from APR to APY, compound the periodic rate across the year: APY = (1 + APR/n)^n − 1, where n counts how often it compounds. At 5% APR monthly that gives 5.116%. To reverse it, APR = n × ((1 + APY)^(1/n) − 1): a 5.000% target APY compounded monthly needs a 4.889% nominal APR. For continuous compounding the pair simplifies to APY = e^APR − 1 and APR = ln(1 + APY). Enter either figure and the tool returns the other.
Is APY always higher than APR?
Almost always, and never lower. APY equals APR only under annual compounding, where interest is added just once and there is nothing to compound within the year. Compound more often — semiannual, monthly, daily — and the APY edges above the APR. The one other tie is a 0% rate: with no interest either way, the two coincide and the gap is nothing. Any rate above zero that posts more often than yearly opens a positive spread, so the APY is the figure that runs ahead.
Why do banks show APY on savings but APR on loans?
Each institution quotes the number that looks better for it. On a deposit you want the yield to seem large, so banks advertise APY — the higher figure. On a loan or card the lender wants the rate to seem small, so it leads with APR — the lower figure — even though a carried balance may compound at the higher effective yield. It is the same compounding math, opposite sides of your wallet. Converting both quotes to APY puts every offer into the same units so you can compare them fairly.
Does the gap actually matter?
At low rates it is small; at high rates it bites. On a $10,000 deposit at 5% APR monthly the spread is only 0.116 points — about $11.62 the first year. But a credit card at 22% APR monthly carries a 2.360-point spread, or 236 basis points. On a $6,000 carried balance that turns a $1,320.00 sticker cost into $1,461.58 of real interest in one year — $141.58 hidden by the APR label. The higher the rate and the more often it compounds, the more the gap costs you.
Is this APR the same as the APR disclosed on a loan?
No. This tool uses the plain nominal APR — pure compounding math with no costs folded in. A loan's disclosed APR under the Truth in Lending Act bakes in points, origination charges, and other fees, so it comes out higher than the nominal rate on the same loan. Do not treat the two as interchangeable: enter a nominal rate here, and use the lender's TILA figure only when you are comparing the all-in cost of competing loan offers. This calculator is about compounding, not fees.
Does this apply to my car loan or mortgage?
Not for the cost figures. Car loans and mortgages amortize — you pay them down on a schedule, so the balance shrinks and interest is charged on a falling amount, using the disclosed loan APR. This tool's borrower cost instead assumes a revolving, non-amortizing balance that is carried and compounds, like an unpaid card or line of credit. You can still use the APR-to-APY conversion for any rate, but the dollar cost shown here describes carried balances, not installment loans being repaid over time.
What compounding do savings accounts actually use?
Most deposit accounts compound daily and credit interest monthly, and some compound monthly; continuous compounding is a mathematical ceiling, not something real accounts actually offer. Frequency matters: 5% APR yields 5.000% APY compounded annually, 5.116% monthly, and 5.127% daily — with continuous compounding as the ceiling, also about 5.127%. The differences are small at ordinary savings rates but real. Check the account's stated frequency, or simply compare the quoted APYs directly, since APY already folds the frequency in and lets you skip the conversion entirely.
What happens at a 0% rate?
Nothing compounds, so APR and APY are both zero and the spread disappears. There is no interest to earn on a deposit and none to owe on a balance, no matter how often the account would otherwise compound. Zero is the one case, aside from annual compounding, where the two labels always match. It also makes a handy sanity check: if a conversion ever shows a gap between APR and APY at a 0% rate, something in the numbers is wrong.
What is continuous compounding here?
It is the limit of compounding infinitely often, and it sets the highest APY any given APR can reach. The formulas simplify to APY = e^APR − 1 and APR = ln(1 + APY). At 5% APR it produces a 5.127% APY — essentially the same as daily, because the gains from compounding ever more frequently shrink quickly. Select it to see the ceiling for a rate. Real accounts rarely compound more often than daily, so continuous compounding is mostly a useful reference point rather than a product you will be offered.
Can I use a custom compounding frequency?
Yes. Besides the preset schedules — annual, semiannual, quarterly, monthly, weekly, and daily — you can enter any number of periods per year, and the tool applies APY = (1 + APR/n)^n − 1 with your n. This is handy for oddities like a rate compounded 26 times a year (biweekly) or 24 times (semimonthly). A higher n always raises the APY, but with diminishing returns as you approach the continuous ceiling, so beyond daily the extra gain is tiny.
What does this tool leave out?
Fees, taxes, and inflation — all of them. It is a pure rate-and-compounding calculator, so it will not subtract account maintenance fees, monthly service charges, tax on interest earned, or the erosion of purchasing power over time. It also assumes the deposit or carried balance stays put, with no added deposits, withdrawals, or payments. Treat its figures as the clean interest math; your real earnings or costs will differ once those real-world items are applied. For carried balances in particular, any payment you make changes the picture.
How does the first-year gap relate to the spread?
Exactly, in year one. Simple interest at year 1 is amount times APR and compound interest is amount times APY, so the dollar gap between them is amount times the spread precisely. On $10,000 at a 0.116-point spread that is $11.62 — matching the $511.62 compounded against $500.00 flat. Beyond year one the gap grows faster than the spread alone, because compounding stacks on prior compounding: over five years the difference reaches $333.59, not five times $11.62. The spread sets the first step; compounding widens every step after.
Which number should I trust when comparing offers?
The APY, always — it is the effective yield that already includes compounding, so two APYs are directly comparable no matter how each offer compounds. Comparing stated APRs can mislead, because a higher APR that compounds less often can end up below a lower APR that compounds daily. Convert every quote to APY first, then rank them. For a deposit, the higher APY wins because you earn more; for a carried balance, the lower APY wins because it costs you less. Same figure, opposite direction of preference.