APY Calculator
Convert APR to APY, or APY back to APR, for daily, monthly or continuous compounding, and work out a CD's value at maturity and the cost of breaking it early.
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About this toolWhat is the APY Calculator?
APY (annual percentage yield) is the rate a savings account or CD actually earns in a year once compounding is counted. APR is the nominal rate before compounding. This APY calculator converts in either direction for any compounding frequency, from annual to daily and continuous, and lists every frequency side by side so you can see how little or how much compounding adds.
The second panel is a CD calculator. Enter a deposit, the rate the bank quotes (as APY or APR), the compounding and the term in months to get the maturity value and the interest earned, with a month-by-month balance. Add the bank's early-withdrawal penalty and a month you might need the money, and it estimates what you would walk away with.
- APR to APY and APY to APR in both directions
- Annual through daily compounding plus continuous
- Table of every frequency for the same rate
- CD maturity value with a balance schedule
- Early-withdrawal penalty estimate for any month
How to use the APY Calculator
- In the converter, choose whether you know the APR or the APY, type the rate and choose the compounding frequency.
- Read the converted rate and the table of every frequency.
- In the CD panel, enter the deposit, the term in months and the rate, and say whether that rate is an APY or an APR.
- Enter the early-withdrawal penalty in months of interest and the month you might withdraw.
- Read the maturity value, the interest and the early-withdrawal estimate, then copy or share the result.
Worked examples
High-yield savings rate
Input
APR 4.5%, compounded daily
Output
APY 4.6025%
Daily compounding adds about a tenth of a point. The same APR compounded monthly gives 4.5940%, and continuously 4.6028%.
One-year CD
Input
$10,000 at 4.25% APY, daily compounding, 12 months, 3-month penalty
Output
$10,425.00 at maturity; withdrawing at month 6 returns about $10,106.23 after a $104.06 penalty
Entering the APY means the full-term interest is exactly 4.25%. The penalty is three months of simple interest at the equivalent 4.16% APR.
Five-year CD broken after a year
Input
$25,000 at 4% APR monthly, 60 months, 12-month penalty, withdraw at month 12
Output
$30,524.91 at maturity (4.074% APY); about $25,018.54 if withdrawn at month 12
A full year's interest penalty wipes out almost everything earned in the first year. Long CDs are only worth their rate if you are confident you will not need the money.
Background and insight
The conversion is APY = (1 + APR / n)^n − 1 for n compounding periods a year, and e^APR − 1 for continuous compounding. A 4.5% APR compounded daily is a 4.6025% APY; compounded monthly it is 4.5940%; compounded continuously it is 4.6028%. The jump from annual to monthly matters, but daily and continuous are almost identical, so a "continuously compounded" headline adds very little.
US banks must quote deposit yields as APY under the Truth in Savings Act, implemented by Regulation DD. Its Appendix A formula is APY = 100 × [(1 + interest / principal)^(365 / days in term) − 1]. For a year-long term that is exactly the compounding formula above, and the calculator's regression tests reproduce the regulation's own worked examples, such as $61.68 of interest on $1,000 over 365 days giving 6.17%.
Because banks advertise APY, the CD panel takes an APY by default and converts it to the matching APR for the compounding you select. That way a 12-month CD earns exactly the advertised percentage, whichever compounding the bank uses. Enter APR instead when your agreement quotes the nominal rate.
Common use cases
Comparing savings accounts
Turn rates quoted different ways into APY so you are comparing like with like.
Choosing a CD term
See the interest on 6, 12 and 24-month CDs and what an early exit would cost.
Checking a bank disclosure
Confirm that an advertised APY matches the stated rate and compounding.
Studying for finance exams
Check effective annual rate problems, including continuous compounding.
Tips and limitations
- APY on deposits and APR on loans are not opposites in marketing: lenders prefer to show the lower APR, savers' products the higher APY.
- Early-withdrawal penalties vary widely. Some are counted in days of interest, and some banks can take them from principal if you withdraw before enough interest has accrued.
- Brokered CDs are not redeemed early by the bank; you sell them on the market, so you can get more or less than the balance shown here.
- Interest on CDs and savings is taxable in the year it is credited in most countries, even when it stays in the account until maturity.
- Variable-rate accounts change their rate; the projection assumes the rate you enter holds for the whole term.
Frequently asked questions
What is the difference between APR and APY?
APR is the nominal yearly rate without compounding. APY includes the effect of interest earning interest during the year. A 5% APR compounded monthly is a 5.116% APY. The more often interest compounds, the bigger the gap, but it is always small at savings-account rates.
How do you calculate APY from an interest rate?
Divide the rate by the number of compounding periods, add 1, raise it to the number of periods and subtract 1: APY = (1 + r / n)^n − 1. For continuous compounding use e^r − 1. The converter does both and shows every common frequency.
How much interest will a $10,000 CD earn in a year?
At 4.25% APY it earns exactly $425 over 12 months, whichever compounding the bank uses, because APY already includes compounding. At 4.25% APR compounded daily it would earn about $434.
Is daily compounding much better than monthly?
Not by much. At 4.5% the APY is 4.5940% with monthly compounding and 4.6025% with daily, a difference of under one hundredth of a percent on the balance. The rate itself matters far more than the compounding frequency.
How is a CD early-withdrawal penalty calculated?
Usually as a number of days or months of interest at the CD's rate on the amount withdrawn, for example 90 days on a one-year CD or 12 months on a five-year CD. The calculator estimates months of simple interest; your account agreement has the exact rule.
What does continuous compounding mean?
It is the limit as the number of compounding periods goes to infinity, giving APY = e^APR − 1. At 4.5% that is 4.6028%, only 0.0003 points above daily compounding, so it is mostly of theoretical interest.
Is there an in-depth guide to the APY Calculator?
Yes. “APY, Bond Yields and SIP Returns: Reading the Rate Correctly” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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