Article — APY Calculator
APY Calculator: Convert APR to Annual Percentage Yield
A 5.00% APR with daily compounding produces an APY of 5.127%. On a $10,000 deposit, that 12.7 basis points of extra yield translates to $12.71 of additional interest in the first year. Every US bank is required by the Truth in Savings Act (12 CFR 1030) to disclose APY using a federally standardized formula.
This calculator implements that exact formula: APY = (1 + r/n)n − 1, where r is the nominal annual rate and n is the number of compoundings per year. It also supports continuous compounding (APY = er − 1) and shows the multi-year balance growth that turns small APY differences into real money over time.
What is APY?
APY (Annual Percentage Yield) is the effective annual rate of return on a deposit account after compounding is factored in. It tells you what your money actually earns over one year, expressed as a percentage. A 5% APY means $10,000 grows to $10,500 in twelve months — guaranteed by federal disclosure standards.
The key word is "effective." Compounding causes interest to earn interest, so a stated 5% nominal rate (APR) compounded daily produces more than $500 of yearly interest on $10,000. The APY captures that. The Federal Reserve standardized the disclosure in 1991 specifically so consumers could compare savings products without unpacking compounding math themselves.
APY vs. APR
APR (Annual Percentage Rate) is the nominal rate before compounding. APY is the effective rate after compounding. They are related but not interchangeable. For an account with annual compounding (n=1), APR equals APY. For any other compounding frequency, APY is greater than APR — sometimes by a fraction of a basis point, sometimes by tens of basis points at higher rates.
The convention in US banking is: deposit products (savings accounts, CDs, money markets) advertise APY; loan products (mortgages, credit cards, auto loans) advertise APR. The asymmetry makes the comparison easy: high APY means more money in, while high APR means more money out. Always shop deposits by APY and loans by APR.
The Truth in Savings Act of 1991 was a direct response to consumer confusion in the late 1980s. Banks were quoting "interest rates" that meant different things — some compounded daily, others quarterly — and customers had no way to compare. Congress fixed it by mandating a single, federally-defined APY disclosure on every deposit account.
The APY formula and the Truth in Savings Act
The formula is defined in 12 CFR 1030 Appendix A, which implements the Truth in Savings Act (Public Law 102-242). For accounts with finite compounding periods: APY = (1 + r/n)n − 1, where r is the nominal annual rate as a decimal and n is the number of compounding periods per year. For continuous compounding: APY = er − 1.
Banks must disclose APY before account opening, on every periodic statement, and in any advertising that mentions an interest rate. The formula is fixed — banks cannot use a different math or round differently. That gives consumers a hard apples-to-apples comparison across institutions and products.
Daily (1 + r/365)365 - 1Monthly (1 + r/12)12 - 1Quarterly (1 + r/4)4 - 1Annual r (no change)Continuous er - 1Reverse APY→APR n[(1+APY)1/n - 1]APY by compounding frequency
The frequency of compounding determines how big the APR-to-APY gap becomes. At 5% APR with annual compounding, APY equals 5.00%. With semi-annual compounding, APY rises to 5.0625%. Quarterly: 5.0945%. Monthly: 5.1162%. Daily: 5.1267%. The jumps get smaller as frequency increases — the gain from monthly to daily is only about 1 basis point.
For most consumers, the choice between monthly and daily compounding is essentially cosmetic. The real money is in choosing high-APY accounts. A 4.50% APY online savings account beats a 0.50% APY traditional savings account by 400 basis points — about $400 per year on $10,000. That dwarfs any difference attributable to compounding frequency at a single bank.
Continuous compounding APY
Continuous compounding is the mathematical limit as compounding frequency approaches infinity. The formula simplifies to APY = er − 1, where e is Euler's number (about 2.71828). At 5% APR, continuous APY is 5.1271% — just 0.0004 percentage points above daily compounding.
Continuous compounding is rarely offered on consumer deposit accounts. You see it mostly in fixed-income mathematics, derivatives pricing, and theoretical finance. For practical APY shopping, daily compounding is the effective ceiling — any further increase in frequency yields negligible additional return.
Typical APY on savings accounts and CDs
As of 2026, online high-yield savings accounts pay 4.00-5.25% APY. Traditional brick-and-mortar banks (Bank of America, Chase, Wells Fargo) pay 0.40-0.60% on their standard savings tiers. The 400-basis-point gap reflects the cost difference: online banks have no branches and pass much of the savings to depositors.
Certificates of Deposit (CDs) lock in a rate for a fixed term. As of early 2026, 12-month CDs at major online banks pay 4.50-5.50% APY; 5-year CDs typically pay slightly less (4.00-4.75%) because the yield curve is flat or slightly inverted. Money market accounts blend savings-account flexibility with CD-like rates, currently paying 4.25-5.25% APY at online institutions.
- Truth in Savings Act = 1991 law mandating APY disclosure
- 12 CFR 1030 = current implementing regulation (Regulation DD)
- APY formula = (1 + r/n)n − 1 for finite compounding
- Continuous APY = er − 1 (theoretical maximum)
- FDIC limit = $250,000 per depositor, per bank, per ownership category
- 5% APR daily compounding = 5.127% APY
- Rule of 72 doubling = 72 ÷ APY% ≈ years to double
- Online vs. traditional gap ≈ 400 basis points (2024-2026)
FDIC insurance and APY protection
FDIC deposit insurance covers up to $250,000 per depositor, per bank, per ownership category. That includes both principal and accrued interest the moment it posts. If your account earns 5% APY and you hit $250,000 in principal-plus-interest, anything above that ceiling is uninsured at that bank. The fix is to split deposits across multiple banks or across ownership categories (individual, joint, retirement, trust).
Federal credit unions get equivalent coverage from the NCUA (National Credit Union Administration) Share Insurance Fund — the same $250,000 limit, the same categories. Both FDIC and NCUA insurance kick in automatically the moment a deposit is made; there are no forms to fill out and no premium for the depositor.
Common APY mistakes
The biggest mistake is comparing APR at one bank to APY at another. Always compare APY to APY. The second mistake is assuming APY is fixed: variable-rate accounts (savings, money market) can change APY any day. Only CDs lock the rate for the term. The third is ignoring minimum balance requirements — many high-yield accounts pay the headline APY only above a threshold like $5,000 or $25,000.
The fourth mistake is missing the introductory-rate trap: some banks advertise a juicy APY for the first 90 days and drop to a much lower standard APY afterward. Read the disclosure for the post-promotional rate before committing significant funds. The fifth is over-concentration: deposits above $250,000 at a single bank lose FDIC coverage on the excess.
Savings account APYs follow the Federal Reserve's target rate with a lag of 1-4 weeks. When the Fed cuts rates by 50 bps, expect your savings APY to drop by 30-45 bps within a month. The 5.00% APY you opened today may be 4.25% by next year if the Fed eases. CDs lock the rate; savings accounts do not.
Build a CD ladder to lock in current high APYs while keeping some liquidity. Open four CDs with 3, 6, 9, and 12-month terms. Every 3 months, one matures and you can either reinvest at the current rate or use the cash. You get most of the rate benefit of a 12-month CD with a fraction of the lock-up risk.