APY on a CD is calculated with the formula APY = 100 × [(1 + r/n)n − 1], where r is the nominal interest rate written as a decimal and n is the number of times the bank compounds interest each year. The formula takes the advertised rate, slices it into the small amount applied during each compounding period, and stacks those periods on top of each other for a full year. The result is the real annual return once interest has had the chance to earn interest on itself.
Why APY Is Higher Than the Stated Rate
Every CD has two rates working behind the scenes. The nominal interest rate is the number on the advertisement. The APY is what you actually earn after compounding is factored in. Compounding is interest earning interest: when the bank credits interest to your balance, the next round of interest is calculated on that larger number.
How often this happens matters. A CD that compounds daily gives your interest 365 chances per year to start generating its own earnings. Monthly compounding does this 12 times, quarterly four times, semi-annually twice. The more frequent the compounding, the more your money grows beyond what the nominal rate alone suggests. Two CDs with identical 5.00% nominal rates can pay different amounts if one compounds daily and the other quarterly. APY collapses that difference into a single number you can compare directly.
The APY Formula
The standard formula for converting a nominal rate into APY is:
APY = 100 × [(1 + r/n)n − 1]
In this formula, r is the nominal interest rate expressed as a decimal (5.00% becomes 0.05) and n is the number of compounding periods per year. Common values for n:
- Daily: n = 365
- Monthly: n = 12
- Quarterly: n = 4
- Semi-annually: n = 2
The logic is straightforward once you break it apart. Dividing r by n gives you the slice of interest applied during each compounding period. Adding 1 represents your original dollar of principal. Raising that sum to the power of n simulates a full year of compounding cycles stacking on each other. Subtracting 1 strips the original dollar back out so you’re left with just the growth. Multiplying by 100 converts the decimal into a percentage.
A Worked Example at 5.00% With Daily Compounding
Take a CD offering a 5.00% nominal rate that compounds daily. The math runs like this:
Divide the decimal rate by the number of compounding periods: 0.05 ÷ 365 = 0.00013699. That is the interest applied each day.
Add 1 to get 1.00013699. That represents one dollar of principal plus one day’s interest.
Raise the result to the 365th power: 1.00013699365 = 1.05127. A full year of daily compounding turns each dollar into about $1.0513.
Subtract 1 to isolate the growth: 1.05127 − 1 = 0.05127.
Multiply by 100: 0.05127 × 100 = 5.13%.
So a 5.00% nominal rate compounded daily works out to an APY of about 5.13%. On a $10,000 deposit held for one year, that 0.13 percentage-point gap is roughly $13 in extra earnings beyond what the nominal rate alone would deliver. The gap widens with higher rates and larger balances.
How Compounding Frequency Changes the Answer
Hold the nominal rate at 5.00% and change only n. Daily compounding (n = 365) produces the 5.13% APY calculated above. Monthly compounding (n = 12) produces a slightly lower APY. Quarterly (n = 4) produces a lower one still. Semi-annual compounding (n = 2) sits lowest among the common schedules. The nominal rate stayed the same in every case; only the compounding frequency moved, and the APY moved with it. This is why the compounding schedule on your disclosure is as important as the headline rate.
The Formula Banks Use for Official Disclosures
The textbook formula explains the relationship between nominal rate and APY. The version banks must use for regulatory disclosures under Regulation DD looks a little different:
APY = 100 × [(1 + Interest/Principal)(365/Days in term) − 1]
Here, Interest is the total dollar amount of interest earned over the CD’s term, Principal is the amount deposited, and Days in term is the actual length of the CD in days.1Consumer Financial Protection Bureau. Appendix A to Part 1030 — Annual Percentage Yield Calculation Rather than working forward from the nominal rate, this version works backward from the actual interest paid and annualizes it.
For a one-year CD (365 days), the exponent becomes 365/365 = 1 and the formula simplifies to APY = 100 × (Interest/Principal). For shorter-term CDs, the exponent stretches the return out to a full-year equivalent so a six-month CD and a two-year CD can be compared on equal footing. In a leap year, banks may use 366 days instead of 365.2eCFR. 12 CFR Part 1030 – Truth in Savings (Regulation DD) Applied correctly, both formulas produce the same APY. The textbook version is easier to reason about. The Regulation DD version is what appears in the fine print.
APY vs. the Nominal Rate on Your Disclosure
Because APY includes compounding, it will always be equal to or higher than the nominal rate on a deposit account. A 5.00% nominal rate with daily compounding produces a 5.13% APY. The two numbers appear side by side on your CD disclosure precisely so you can see the gap compounding creates. Federal law requires banks to advertise deposit products using APY rather than APR, so comparisons across institutions and compounding schedules land on the same measurement.
Why Your Real Return Can Still Fall Short of the APY
The APY on your disclosure assumes you hold the CD to maturity. Cash out early and the bank charges a penalty that comes directly out of your return. Typical penalties run around three months of interest on a one-year CD and six to twelve months of interest on a five-year CD, though every bank sets its own terms. Withdraw early enough and the penalty can exceed the interest you have earned and reach into your principal, which means a CD advertising a 5.13% APY can end up delivering a negative effective return.
Taxes also sit between the APY and what you keep. CD interest is taxed as ordinary income at your federal marginal rate, and you owe tax in the year interest is credited to the account, even if you leave it in the CD. The APY describes the gross yield the account produces, not the after-tax amount in your pocket.