When a bank quotes you an interest rate, it is almost never the whole story. The Annual Percentage Rate (APR) is the nominal, headline rate; the Annual Percentage Yield (APY) is what you actually pay or earn once compounding is folded in. On a loan, the gap between them is money leaking out of your pocket. On a savings account, the gap is money quietly growing while you are not looking. This APR vs APY calculator converts your quoted nominal rate into the real effective annual yield, then translates the difference into dollars on your principal balance so you can compare offers on equal footing.
Adjust the inputs and every figure updates instantly. Switch the compounding setting from monthly to daily and watch the APY climb — that single choice is why two savings accounts advertised at the same "5%" can leave you with noticeably different balances after a year.
How to Use
- Enter the Annual Percentage Rate (APR) quoted by the lender or shown on your savings statement. This is the nominal, non-compounded rate.
- Type your Principal Balance — the amount you owe on a loan, or the balance you hold in the account. The dollar figures below are calculated on this one-year balance.
- Choose the Compounding frequency. Most consumer loans and basic savings accounts compound monthly (12). High-yield savings accounts often compound daily (365), certificates of deposit may compound quarterly (4), and simple bonds compound annually (1).
- Read the result card. Effective APY is the true annual rate after compounding. The Yield Difference shows how many extra percentage points compounding adds, and the Dollar Gap From Compounding turns that difference into cash over one year.
On a loan, the dollar gap is extra interest you effectively pay beyond the nominal APR. On a deposit, the same gap is extra interest you earn. The math is identical; only the direction of the money changes.
The APR vs APY Formula
The relationship between a nominal annual rate and its effective annual yield comes directly from compound interest:
APY = (1 + APR / n)ⁿ − 1
Where:
- APR is the nominal annual rate, expressed as a decimal (6% becomes 0.06).
- n is the number of compounding periods in a year — 12 for monthly, 365 for daily.
- The term (1 + APR/n) is the growth factor applied each period, raised to the nth power to roll it across the whole year.
Worked example at 6.00% APR, compounded monthly on a $10,000 balance: the monthly rate is 0.06 / 12 = 0.005. Over twelve months, (1.005)¹² = 1.061678, so APY = 6.1678%. On the principal, nominal interest is $10,000 × 0.06 = $600, while compounded interest is $10,000 × 0.061678 = $616.78. The compounding "extra" is $16.78 in one year — small on $10,000, but it scales straight up to $1,678 on a $1,000,000 balance, and it repeats every year.
If the APR is 0%, the formula still holds: (1 + 0)ⁿ − 1 = 0, and every dollar figure is 0. The engine uses that zero-rate fallback rather than dividing by anything unstable.
Why the Two Rates Differ
APR and APY are not competing products; they are two lenses on the same money. APR spreads the rate evenly across the year as if interest never reinvested itself. APY assumes each period's interest is immediately added to the balance and starts earning its own interest — the snowball effect.
The more often interest compounds, the wider the gap. A 10% APR compounded annually stays at 10.00% APY. Compounded monthly it becomes 10.47%; compounded daily it reaches 10.52%. That is why fine print matters: a daily-compounded high-yield savings account pays more than a monthly-compounded one at the identical advertised APR. Federal truth-in-lending rules require lenders to disclose APR for loans, while truth-in-savings rules require banks to disclose APY for deposits — so you naturally see APR when borrowing and APY when saving, which makes this side-by-side conversion genuinely useful.
Examples
Example 1 — A credit card at 23.99% APR. Carrying a $5,000 balance, the nominal interest for a year looks like $5,000 × 0.2399 = $1,199.50. Because credit cards compound daily, the effective APY is about 26.99%, and the real interest charged is near $1,349 — roughly $150 more than the headline rate suggests. That gap is exactly why paying down revolving balances early matters.
Example 2 — High-yield savings at 4.50% APR. Deposit $20,000 in an account that compounds monthly. The APY works out to about 4.594%, earning roughly $918.78 in a year instead of the $900 a flat 4.50% would imply. Switch to a daily-compounding bank at the same 4.50% APR and the APY edges up to about 4.602%, earning a little more still. Use the Compounding selector to compare two banks before moving money.
Example 3 — A $1,000,000 loan at 5.00% APR. Monthly compounding lifts the effective rate to about 5.116%. On the principal, nominal interest is $50,000 but compounded interest is about $51,162 — a $1,162 gap in a single year. On seven-figure financing, choosing a loan with fewer compounding periods or negotiating the APR downward saves real money, and running this number first shows you which lever moves the needle most.
FAQ
What is the difference between APR and APY?
APR is the nominal annual rate shown before compounding; APY is the effective annual yield after interest is compounded and reinvested. On a loan, APR is what lenders are required to advertise (and often includes fees), while on a savings account banks must show APY. APY is always equal to or higher than APR once compounding is more frequent than annual.
How do I convert APR to APY?
Use the formula APY = (1 + APR/n)ⁿ − 1, where n is the number of compounding periods per year. For monthly compounding, divide the APR by 12, add 1, raise that to the 12th power, and subtract 1. Enter your APR and choose your compounding frequency above and the calculator does this instantly.
Is a higher APY better when I am saving?
Yes, for deposits a higher APY means more interest credited to your account over the year, all else equal. Two accounts advertised at the same nominal APR can have different APYs depending on compounding frequency — daily compounding always beats monthly, which beats annual. Compare APY, not the headline APR, when choosing a savings account or CD.
Is a higher APR worse when I am borrowing?
Yes. On a loan, credit card, or mortgage, a higher APR costs you more interest, and compounding pushes the true effective rate even higher. The dollar gap shown on this page is the extra cost created by compounding; a lower APR and less frequent compounding both reduce it.
Does compounding monthly or daily matter that much?
The difference is small in percentage points but grows with large balances and long horizons. At 10% APR, monthly compounding gives about 10.47% APY while daily gives about 10.52% — half a point. On $10,000 that is a few dollars a year; on $1,000,000 over ten years it becomes thousands of dollars. Set the Compounding selector to match your actual account terms.
What does the dollar gap from compounding actually mean?
It is the one-year difference between interest calculated at the nominal APR and interest calculated at the effective APY on your principal. If you are saving, it is the extra interest compounding earns for you. If you are borrowing, it is the extra interest compounding charges you beyond the advertised rate.
Why do lenders show APR but banks show APY?
US law mandates it: truth-in-lending rules require APR disclosure so borrowers can compare loan offers including fees, while truth-in-savings rules require APY so depositors can compare what an account actually yields. Showing both for the same balance removes the apples-to-oranges mismatch.
Disclaimer
This APR vs APY calculator is provided for informational purposes only and does not constitute financial, lending, or investment advice. Effective yields are computed from the standard compound-interest formula using the inputs you enter; actual account terms, fee adjustments, compounding conventions, and promotional rates vary by institution. Always confirm the disclosed APY or APR directly with your lender or bank before making a borrowing, saving, or investing decision.