APR (Annual Percentage Rate)
APY (Annual Percentage Yield)
Nominal Rate
Effective Difference
Table of Contents
APR vs APY: Compare Rates on Equal Terms
The same nominal interest rate can produce very different actual returns depending on how often it compounds. APR strips out compounding, APY includes it — which is why "5% APR" and "5% APY" are not the same thing. This calculator converts cleanly between APR, APY and the underlying nominal rate at any compounding frequency.
Use it to compare savings accounts, CDs, credit cards and loans on a true apples-to-apples basis.
APR vs APY: what is the difference?
APR (Annual Percentage Rate) and APY (Annual Percentage Yield) both describe an annual interest rate, but they handle compounding very differently. APR is the simple annual rate — it ignores how often interest is added to the balance during the year. APY captures the effect of compounding, showing the actual percentage growth of a balance over a full year.
For the same loan or account, APY is always equal to or higher than APR. They are equal only when interest compounds exactly once per year. The more frequently interest compounds, the bigger the gap. A 6% APR compounded monthly produces an APY of 6.17%, while compounded daily it produces 6.18%. The difference looks small in percentage terms but compounds significantly over multi-year periods on large balances.
Why this distinction matters
Banks and lenders use these terms strategically. Savings products are advertised by APY because that is the higher number — it makes returns look better. Loans are advertised by APR because it is the lower number — and because federal Truth in Lending law requires it, with the goal of giving borrowers a more honest cost of borrowing that includes most fees.
If you are comparing two financial products, always compare them on the same basis. If one quotes APR and the other APY, convert one so they are directly comparable. Otherwise the higher-compounding product may look worse than it actually is, or vice versa.
Conversion formulas
Converting APR to APY: APY = (1 + APR/n)n − 1, where n is the number of compounding periods per year. For continuous compounding, the formula simplifies to APY = eAPR − 1.
Converting APY to APR: APR = n × ((1 + APY)1/n − 1). For continuous compounding, APR = ln(1 + APY).
The "nominal rate" is the same as APR in most contexts. Both refer to the stated annual rate before compounding effects are applied.
How compounding frequency changes results
Take a 5% nominal rate. Compounded annually, it produces a 5.00% APY. Compounded semi-annually, 5.06%. Quarterly, 5.09%. Monthly, 5.12%. Daily, 5.13%. Continuously, 5.13% (the theoretical maximum). Each step increases the effective yield, but the gains shrink quickly — going from monthly to daily compounding adds only about one basis point.
For practical purposes, monthly and daily compounding produce very similar results. Most credit cards compound daily on the average daily balance. Most mortgages compound monthly. Most savings accounts and CDs use either daily or monthly compounding, with daily being the most common.
How APR works on loans
For loans, APR is more than just the interest rate — it includes most lender fees expressed as an annualized percentage of the loan amount. This is why the APR on a mortgage is typically slightly higher than the quoted interest rate, especially when the loan involves origination fees or discount points.
The APR is the most useful single number for comparing loan offers because it reflects most of the actual cost of borrowing. A loan with a slightly higher rate but no fees may have a lower APR than a "low rate" loan with significant fees baked in. Always look at APR side by side, not just the headline interest rate.
How APY works on savings
For savings accounts, CDs and money market accounts, APY tells you exactly how much your balance will grow in one year, assuming no deposits or withdrawals. A 5.00% APY means $10,000 grows to $10,500 over one year, regardless of compounding frequency. That is the entire point — APY normalizes compounding so different products can be compared on a single number.
When shopping for high-yield savings or CDs, always look at APY rather than the nominal rate. Two products with the same nominal rate but different compounding schedules will produce different actual returns. APY removes the guesswork.
FAQs
APR (Annual Percentage Rate) is the simple annual interest rate without accounting for compounding. APY (Annual Percentage Yield) includes the effect of compounding over a year. For the same nominal rate, APY is always equal to or higher than APR — and the difference grows with more frequent compounding. APR is typically used to describe loans; APY is typically used to describe savings.
The conversion formula is APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year. For example, a 6% APR compounded monthly (n=12) becomes APY = (1 + 0.06/12)^12 − 1 = 6.17%. The more frequently interest compounds, the bigger the gap between APR and APY.
The reverse conversion is APR = n × ((1 + APY)^(1/n) − 1). For a 5% APY compounded monthly, APR = 12 × ((1.05)^(1/12) − 1) ≈ 4.89%. APR is always lower than (or equal to) APY when both describe the same investment, because it strips out the compounding effect.
More frequent compounding means interest is added to the balance sooner, and that interest immediately starts earning interest of its own. The same 5% nominal rate produces different effective yields depending on whether it compounds annually, monthly, daily or continuously. Daily compounding is common for savings accounts; monthly is typical for credit cards and mortgages.
Loans are conventionally compared by APR because APR includes most fees and lender costs, providing a more apples-to-apples view of the total borrowing cost. Two loans with the same APY but different fees can have meaningfully different APRs. Federal Truth in Lending laws require lenders to disclose APR for this reason.
Savings accounts and CDs are best compared by APY because it reflects what you will actually earn after compounding over a year. A 5.00% APY account always earns more than a 4.95% APY account, regardless of how each one's nominal rate or compounding schedule is structured. Federal Truth in Savings rules require banks to disclose APY for the same reason.