APR to APY Calculator
Banks quote APR to keep loan costs sounding low, while savings accounts advertise APY to make yields look high — this tool converts between the two so you can see what compounding actually does to your money.
Lenders quote APR. Savings accounts advertise APY. Same money, different math.
How to Use This Calculator
-
1
Choose your conversion path
Hit "APR → APY" when looking at a loan or card offer. Switch to "APY → APR" to strip compounding out of an advertised savings yield.
-
2
Enter the stated percentage
Type the percentage from your paperwork. Don't worry about turning 24% into 0.24 — the form converts decimals automatically as you type.
-
3
Matching the compounding cycle
Check your disclosure for how often interest compounds. Cards and savings accounts usually compound daily or monthly, while bonds stick to semiannual schedules.
-
4
Check the spread
Your effective rate appears right away alongside the percentage-point gap, showing the exact penalty or bonus compounding creates over twelve months.
The Formula
Lenders prefer APR because it ignores compounding and treats interest as a flat annual fee. APY reflects reality by including every time unpaid interest gets added to your principal:
APY = (1 + (APR / n))^n − 1
APR = n × ((1 + APY)^(1 / n) − 1)
- APR Annual Percentage Rate as a decimal (e.g. 24% becomes 0.24).
- APY Annual Percentage Yield as a decimal (e.g. 26.82% becomes 0.2682).
- n Compounding periods per year (365 daily, 12 monthly, 4 quarterly, 2 semiannual, 1 annual).
Frequent compounding widens this spread because interest adds to your balance earlier, giving subsequent cycles a larger base to multiply against.
Example Scenarios
Most of us only notice the compounding spread after signing paperwork. Not a big loan myself yet — but I've watched family members sign paperwork where the only number discussed was the monthly amount, and the rate's fine print went completely unread. Here's the arithmetic for both directions:
Scenario 1: A credit card balance at 24% APR compounded monthly
Your card agreement states 24% APR compounded monthly (n = 12). Here's how that turns into the true APY:
- Divide the rate by 12 periods: 0.24 / 12 = 0.02 (a 2% monthly charge).
- Add 1 to the periodic rate: 1 + 0.02 = 1.02.
- Raise that to the 12th power: (1.02)^12 ≈ 1.268242.
- Subtract 1 and multiply by 100: 0.268242 × 100 = 26.82% APY.
That 2.82 percentage-point bump is why carrying card debt stings harder than the headline rate suggests.
Scenario 2: A savings account paying 5.13% APY compounded daily
A bank advertises 5.13% APY on savings with daily compounding (n = 365). To find their base annual rate, run it backwards:
- Turn APY into a decimal and add 1: 1 + 0.0513 = 1.0513.
- Take the 365th root: (1.0513)^(1 / 365) ≈ 1.00013698.
- Subtract 1 to get the daily rate: 0.00013698.
- Multiply by 365 days: 0.00013698 × 365 ≈ 0.0500, or 5.00% APR.
The bank advertises 5.13%, but their underlying annual interest engine runs at an even 5.00%.
Frequently Asked Questions
What's the difference between APR and APY?
APR is simple interest ignoring compounding. APY includes interest earned on interest, showing your true annual return or borrowing cost.
Which one should I actually compare?
Compare APR to APR for loans, and APY to APY for savings. Mixing them makes bad offers look cheap. The one I calculate myself — advertised numbers are picked to flatter the product, and after building this tool I know exactly how far the real rate can drift from the headline. If two loans use different cycles, convert both to APY to judge them fairly.
Why is APY always higher than APR?
Compounding adds unpaid interest to your balance, so future cycles multiply against a larger sum. Faster compounding expands that gap, but annual compounding leaves both rates identical.
Do credit cards use APR or APY?
Card agreements quote APR by law, but issuers compound interest daily. If you carry a monthly balance, what you actually pay mirrors the higher APY.
What compounding frequency do banks usually use?
Most banks compound savings and CDs daily, crediting interest monthly. Mortgages and car loans compound monthly, while corporate bonds typically pay semiannually.