APR to APY Calculator

APR and APY are the same interest, counted differently

APR is a nominal rate: the periodic rate multiplied by the number of periods in a year, with no allowance for interest earning interest. APY (the effective annual rate, sometimes written EAR) is what you actually end up with after that compounding happens. The gap between them is created entirely by the compounding frequency, which is why a single 5% figure can mean four slightly different things depending on the fine print.

The maths is short. Going from nominal to effective: APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year. Going back the other way: APR = n × ((1 + APY)^(1/n) − 1). When compounding is continuous the formulas collapse to APY = e^APR − 1 and APR = ln(1 + APY). Set n to 1 and both formulas return the input unchanged — annual compounding gives you nothing to compound.

Worked example 1: comparing two savings accounts

Bank A advertises 4.85% APR compounded monthly. Bank B advertises 4.80% APY. The headline numbers say A wins, but they are not the same unit, so convert first. For A: 4.85/12 = 0.404167% a month, and (1.00404167)^12 − 1 = 4.959%. That is A's true APY, which does beat B's 4.80% — but by 0.159 percentage points, not the 0.05 the raw comparison suggested. On a $25,000 balance held for a year that is ,239.82 with A against ,200.00 with B: roughly $40 a year. Always restate both offers as APY before choosing.

Worked example 2: what a credit card really costs

A card quoting 22.9% APR almost always compounds daily on the average balance. Convert it: (1 + 0.229/365)^365 − 1 = 25.725% APY. Carry $5,000 for a full year and you pay about ,286 in interest, not the ,145 the APR implies — an extra 41 that never appears in the advertising. This is the one place where the APR-to-APY gap is large enough to change a decision, and it is also the one place where issuers are permitted to advertise only the APR.

Worked example 3: reversing a quoted APY

A CD offers 5.00% APY and you want to know the nominal rate the bank is actually applying daily. Use the reverse formula: 365 × ((1.05)^(1/365) − 1) = 4.879% APR. That is the number to compare against another bank quoting a daily nominal rate, and it is also the figure you would use in a spreadsheet that compounds day by day.

How much frequency changes the answer

Two things stand out. The frequency effect grows with the square of the rate, roughly, so it is nearly irrelevant on a 2% savings account and material on a 23% card. And most of the benefit arrives by monthly compounding — the jump from monthly to daily is worth about one basis point at 5%. Marketing that shouts about daily compounding on a savings account is selling you a rounding error.

When to use which number

Use APY to compare anything you earn: savings accounts, CDs, money market funds. Use APR to compare the sticker cost of anything you borrow, but convert it to APY when the balance revolves — cards, HELOC draws, and any loan where interest accrues daily on an unpaid balance. For amortising loans such as mortgages and car finance the payment schedule already reflects compounding, so the disclosed APR is the more useful comparison figure there.

Limitations of this calculator

This converts a rate to a rate and nothing else. It does not add annual card fees, origination points, closing costs or account maintenance charges, all of which raise the real cost of borrowing above any APR. It assumes the rate holds for a full year, so promotional and teaser rates — a 5.50% intro APY that drops to 3.00% after six months — need to be blended by hand before conversion. Variable rates are treated as fixed, tiered balances are ignored, and tax on interest earned is not modelled. It also uses a 365-day year for daily compounding; a few institutions use 360, which shifts the effective rate slightly in their favour.