APY Calculator

What APY tells you

APY is the real one-year return you get from a deposit account or fixed-rate product, after compounding has done its work. It is the number to compare between accounts because it neutralizes differences in compounding frequency. Two accounts at the same APY produce the same first-year interest on the same balance, regardless of how often they compound.

How the calculator works

You enter a nominal annual rate and pick a compounding frequency (annually, semi-annually, quarterly, monthly, daily, or continuously). The calculator returns the APY, the gap between APY and the nominal rate (the compounding boost), and the first-year interest on the optional starting balance. A short table shows the APY you would get at the same nominal rate for every frequency option, so you can see at a glance how much compounding matters.

APY vs APR

APR is a Regulation Z figure: the cost of credit as a yearly rate, including finance charges beyond the interest itself. It is not simply the nominal rate, and on a loan it usually exceeds the note rate. APY is the effective annual rate with compounding included. For savings products, you usually want APY. For loans, you usually see APR. When comparing a loan APR to a savings APY, remember that they are measuring different things.

For loan math itself, the loan calculator and mortgage calculator handle the amortization side of compound interest.

Why APY can be higher than the stated rate

When interest is compounded more than once a year, each compounding period adds interest to the balance, and the next period earns interest on that new, larger balance. The result is that the effective rate is a bit higher than the nominal rate. A 5% nominal rate compounded monthly produces an APY of about 5.1162%, because the extra 0.1162 percentage points come from interest earning interest during the year.

Worked example

Nominal rate 5%, monthly compounding, starting balance $10,000.

• Convert nominal rate to decimal: 5% = 0.05
• Apply APY formula: (1 + 0.05 / 12)^12 − 1 ≈ 0.0511618979
• Convert to percent: 5.1162%
• First-year interest on $10,000: 10,000 × 0.0511618979 = $511.62
• Balance after one year: ≈ $10,511.62

The same 5% nominal rate produces an APY of exactly 5.0000% with annual compounding, about 5.0945% with quarterly, 5.1267% with daily, and 5.1271% with continuous. The calculator shows the full table side by side.

Where APY shows up

APY is the headline number for savings products: savings accounts, money market accounts, and certificates of deposit (CDs) advertise APY because it is the easiest fair comparison. APY also shows up on bond funds, treasury products, and some checking accounts. For projecting how a balance grows over many years, the compound interest calculator takes APY-style math out to a longer horizon with optional monthly contributions.

Common mistakes

• Comparing two products by nominal rate when they compound differently. Convert both to APY first.
• Confusing APR with APY. APR is nominal; APY is effective. On a savings product, APY is the one to use.
• Assuming that going from daily to continuous compounding will boost the return noticeably. The difference is fractions of a percent.
• Treating a promotional APY as permanent. Many high-yield accounts revert to a lower rate after a promo window or require a minimum balance to keep the rate.
• Ignoring fees and minimum-balance penalties. They can erase the compounding boost entirely.

What APY is, in the regulation that defines it

APY is not a convention this page invented, and it is not free- floating marketing language. It is a defined term in federal law. Regulation DD, at 12 CFR 1030.2(c), defines annual percentage yield as "a percentage rate reflecting the total amount of interest paid on an account, based on the interest rate and the frequency of compounding for a 365-day period and calculated according to the rules in appendix A of this part". The same part defines the interest rate separately, as "the annual rate of interest paid on an account which does not reflect compounding". Two numbers, two definitions, and a bank must disclose both.

The formula this page runs is not the one the regulation prints. Appendix A gives APY = 100 [(1 + Interest/Principal)^(365/Days in term) − 1], where Interest is the actual dollars earned over the actual term. That annualises a realised amount. This page runs (1 + r/n)^n − 1, which annualises a nominal RATE over a period count. The two coincide when the term is 365 days, which is the case an ordinary savings account without a stated maturity falls into, and that is why the identity is the right tool here. It is still worth knowing they are different expressions.

APY and annual percentage yield earned are not the same number

This is the pair that causes the most confusion, and the difference is tense. APY is FORWARD-looking and assumption-based: Appendix A builds it on principal "assumed to have been deposited" and a rate assumed to hold for a year. Annual percentage yield EARNED is BACKWARD-looking and factual. Appendix A Part II defines it as "an annualized rate that reflects the relationship between the amount of interest actually earned on the consumer's account during the statement period and the average daily balance in the account for the statement period", and 1030.6(a)(1) is what puts it on your statement.

So the number on your statement and the number in the advertisement answer different questions. They will differ whenever your balance moved during the period or the rate changed. This calculator computes the first kind.

The 365-day year, and the leap-year gap

Appendix A states that "the annual percentage yield is expressed as an annualized rate, based on a 365-day year", and then adds that institutions "may calculate the annual percentage yield based on a 365-day or a 366-day year in a leap year".

May, not must. In a leap year two banks with identical products, identical rates and identical compounding can lawfully publish two different APYs, and neither is wrong. It is a small difference and it is a real one, and it is the kind of thing an APY comparison quietly assumes away. This page uses 365 for its daily option.

An APY quote is not a promise, and the regulator says so

APY annualises a rate as though it held for a full year. For a fixed-term product like a CD the rate is contracted for the term, and the quote is close to a promise. For an ordinary savings account it is not: the rate can move the week after you open it, and Regulation DD at 1030.4(b)(1) requires the disclosure to state "the fact that the interest rate and annual percentage yield may change".

That is the regulator's own wording for the thing this page cannot know. The calculator has no view on whether a rate will persist, what the account costs in fees, whether a minimum balance applies, or whether one account is better than another. It multiplies out a rate you supply at a frequency you supply.

Edge cases worth knowing

• Frequency matters less than people expect. At a 5% nominal rate, annual compounding gives 5.0000%, monthly 5.1162%, daily 5.1267% and continuous 5.1271%. The whole journey from ANNUAL to infinitely often is about an eighth of a percentage point, 0.1271. From monthly to infinitely often it is about a hundredth, 0.0109. Chasing daily over monthly compounding is chasing 0.0106 points.
• Fees are outside the arithmetic. A monthly maintenance fee can wipe out the whole compounding advantage on a small balance. APY as defined does not net them out and neither does this page.
• Credit unions use a different word. NCUA's 12 CFR Part 707 mirrors Regulation DD with dividends in place of interest, the same 365-day base and the same leap-year permission. Same arithmetic, different statute.
• APR is not the mirror image. On a loan, APR under Regulation Z includes finance charges beyond the interest, so it usually sits ABOVE the note rate. APY and APR are not the same quantity measured from two sides.

What this page does not know

It converts a nominal rate and a compounding frequency into an APY. It does not know your balance, your bank's fees, its minimum-balance rules, whether the rate is fixed or variable, or what happens to it next month. Nothing here recommends an account or ranks one against another.

Nothing you type leaves this page. The arithmetic runs in your browser. The rate and frequency are not sent to a server, are not written into the address bar, and are gone when you close the tab. There are no accounts and nothing to sign up for.

Related tools

• Compound interest calculator for projecting balance growth over many years with optional monthly contributions.
• Simple interest calculator for non-compounding interest (loans and short-term notes that bill interest only on the original principal).
• CD calculator for fixed-term certificates of deposit using a stated APY.
• Savings calculator for goal-oriented planning that uses the APY directly.
• 401k calculator for employer-sponsored retirement projections with salary growth and employer match.
• Roth IRA calculator for an after-tax retirement account projection.
• Loan calculator for amortized loan payments and total interest.
• Mortgage calculator for principal, interest, taxes, insurance, PMI, and HOA.
• Simple interest vs compound interest explains the two formulas, the difference in growth, and when to use each.
• APR vs interest rate explains how APR and APY differ and which one belongs on which side of a transaction.