APY Calculator — APR ↔ APY Conversion + Earnings on $1,000

What is APY?

APY stands for Annual Percentage Yield— the effective annual rate of return on a deposit account, factoring in the effect of compounding within the year. It is the regulatory standard for advertising savings rates in the United States, mandated by the Truth in Savings Act of 1991 (Regulation DD). When a bank quotes “4.50% APY,” that is the actual percentage your money will grow if you leave it untouched for a full year and the rate doesn’t change.

APY is the savings-side cousin of APR (Annual Percentage Rate), which is the regulatory standard for advertising loan rates under Regulation Z (Truth in Lending Act, 1968). Both describe an annualized rate, but APY tells you what you earn with compounding; APR tells you what you paywithout compounding. For an identical underlying rate, APY is always higher than APR — that’s why banks advertise APY for savings (higher number is more attractive) and APR for credit cards and loans (lower number is more attractive).

This calculator converts both directions: APR → APY(the common case — you know the nominal rate and want to see what it’s actually worth with compounding) and APY → APR(the back-solve case — you want to compare a published APY against an APR-quoted product on the same nominal basis).

The APY Formula

The conversion is a closed-form formula with three inputs:

APY = (1 + APR / n)^n − 1
where APR is the nominal rate expressed as a decimal, and n is the number of compounding periods per year.

The inverse, going from APY back to APR, is:

APR = n × ((1 + APY)^(1/n) − 1)

Five compounding frequencies cover essentially every retail product: annual (n=1), quarterly (n=4), monthly (n=12), weekly (n=52), and daily (n=365). US high-yield savings accounts compound daily, most CDs compound monthly, and a small number of legacy products compound quarterly or annually.

Worked Example: 5% APR vs 5% APY on $10,000

Imagine two products both advertising “5%” — one as APR with monthly compounding, the other as APY (which already includes the compounding):

Three observations from the table:

• Daily compounding beats monthly compounding by only $1.05on a $10,000 balance. Banks marketing “daily compounding” as a major advantage are exaggerating — the difference is real but tiny at typical rates.
• Quoted APY directly tells you what you’ll earn. A 5% APY product credits exactly $500 on $10,000 over a year, regardless of the underlying compounding frequency.
• A 5% APR with daily compounding (5.127% APY) and a 5% APY product (5.000% APY) sound identical to a casual reader, but the APR product is actually 0.127 percentage points better. Always compare APYs, not headline rates.

The Continuous-Compounding Ceiling

What happens as compounding frequency increases without bound? The formula converges to:

APY_continuous = e^APR − 1
where e ≈ 2.71828 (Euler’s constant).

At 5% APR continuous, APY = e^0.05− 1 = 5.127%. Daily compounding already reaches 99.6% of the continuous limit. Second-by-second compounding (n = 31.5 million) reaches 99.999%. After daily, you’re chasing fractions of basis points — which is exactly why no real bank compounds faster than daily. The marginal yield is below the operational cost of computing it.

Continuous compounding is the theoretical limit. Real-world products are bounded by it, never reach it, and at typical retail rates miss it by less than one basis point. If you see a quote claiming “6% continuous yield” on what should be a 6% APR product, the bank is rounding up; reality is closer to 6.184%.

How Compounding Frequency Actually Matters

The spread between APR and APY (i.e., the value of compounding) scales with boththe rate and the compounding frequency. At low rates, frequency is nearly irrelevant; at very high rates, it matters more. Here’s the APY produced by a 1%, 5%, and 15% APR at each common compounding frequency:

At credit-card-typical rates (15-25% APR), monthly compounding produces an APY roughly 3 percentage points higherthan the headline. This is why your credit-card balance grows faster than you’d expect: the interest is compounding monthly (sometimes daily) on the outstanding balance. Theloan EMI calculator uses the underlying APR; the actual cost of carrying a revolving balance reflects the higher APY.

The Regulatory Backstory

APY exists as a regulatory disclosure because, before 1991, US banks could advertise “5% rate, compounded daily” without telling you the effective annual yield. Different banks chose different compounding frequencies and quoted rates that weren’t directly comparable. A “5.0% rate compounded daily” from Bank A and a “5.1% rate compounded annually” from Bank B both produced almost identical actual earnings, but the second number sounded better — and the consumer had to know the compounding math to see through the marketing.

The Truth in Savings Act of 1991 (Regulation DD, enforced by the CFPB and state regulators) forced every US deposit-taking institution to advertise APY rather than nominal rate. The resulting numbers are directly comparable: a 4.50% APY from Bank A and a 4.75% APY from Bank B mean exactly what they look like — Bank B is paying more, full stop.

APY on Real Products

Typical 2026 ranges for the main retail deposit categories:

• High-yield savings accounts (HYSA)— 4.0-5.25% APY at most top-tier online banks (Ally, Marcus, Capital One 360, Bask Bank, SoFi). Daily compounding standard. FDIC-insured up to $250,000.
• Money market accounts— 4.0-5.0% APY, often with check writing and ATM access. Generally tied to a minimum balance ($2,500-$10,000). Daily or monthly compounding.
• Certificates of deposit (CDs)— 4.5-5.5% APY for 12-month terms; lower for shorter terms. Monthly compounding typical. Early withdrawal penalty (90-180 days of interest) applies.
• Treasury bills + I-bonds— 4.5-5.0% rate, typically quoted on a discount basis rather than APY. T-bill effective yield is similar to APY at top HYSAs but with state/local tax exemption — meaningful edge in high-tax states.
• Big-bank checking accounts— 0.01-0.05% APY. Almost always “APY” nominally but functionally zero. The opportunity cost of leaving $50,000 in a big-bank checking instead of a HYSA is roughly $2,500/year.

APY vs Total Return on Investments

Don’t conflate APY with the expected return on a stock-market investment. APY is a statedrate for fixed-yield products (savings, CDs, money markets) — the bank guarantees that yield if the rate doesn’t change. Total return on a stock or ETF is realized after the factand combines price change plus dividends — it varies wildly from year to year, can be negative in any given year, and historically averages 7-10% real (inflation-adjusted) for US equity over multi-decade periods.

A 5% APY savings account is risk-free (FDIC-insured). A “5% expected return” on a stock portfolio is risk-bearing — you might earn 30% this year and lose 25% next year, with the expected long-run average being 5%. Use the compound interest calculator for projecting long-term growth on either, but understand that the underlying products have completely different risk profiles.

Common Mistakes & Edge Cases

• Comparing “rate” to “APY.”A 5.05% rate (APR) with daily compounding produces an APY of about 5.18% — slightly better than a 5.10% APY product. Always compare apples-to-apples; when in doubt, back-solve to APY using this calculator.
• Ignoring after-tax yield. APY is gross. Interest income is reported on IRS Form 1099-INT and taxed as ordinary income at your federal + state marginal rates. At a 24% federal + 6% state bracket, a 5.127% APY translates to a 3.59% after-tax yield. The inflation calculatorcan then translate to real (inflation-adjusted) after-tax yield — the only number that actually measures purchasing-power growth.
• Falling for promotional APY caps.Some “6% APY” checking accounts apply that rate only to the first $5,000 balance; the rest earns 0.05%. A weighted average on $30,000 produces a 1.04% effective APY — nowhere near the marketed number. Always read the balance-tier footnote.
• Confusing APY with bond yield-to-maturity (YTM). Bonds and T-bills are quoted on a discount-yield or YTM basis, not APY. A 5% T-bill is functionally similar to a 5% APY savings, but the math is slightly different and the tax treatment is meaningfully better (state-tax-exempt).
• Forgetting variable-rate accounts can drop.A 5% APY today on a HYSA can be 4% next month if the Fed cuts rates. The APY you see is the rate now — not a guaranteed annual return like a CD. Lock the rate (via CD) if rate-drop risk matters; stay liquid (via HYSA) if it doesn’t.
• Misapplying APY to one-time deposits without contributions.If you’re saving recurring monthly contributions on top of a starting balance, total earned interest is meaningfully more than simply (balance × APY). Use the compound interest calculator for that multi-input case.

Related Calculators

• Compound interest calculator— project a starting balance plus recurring monthly contributions over any number of years at the APY you found here.
• Retirement savings calculator— 401k and IRA growth projections with real expected returns (not deposit APYs).
• Investment ROI— back-solve realized return from start/end values on any investment, fixed-yield or variable.
• Loan EMI calculator— monthly payment math on the loan side; APY equivalents matter for the actual cost of carrying a credit-card balance.
• Inflation calculator— translate APY to real after-inflation yield, the only number that measures actual purchasing-power growth.