APR to APY Calculator

How to use this calculator

Three fields. One required, two optional but useful.

APR (%) — The Annual Percentage Rate you want to convert. This is the nominal yearly rate before compounding is applied. For a savings account or CD, the bank might list this as “interest rate” or “nominal rate.” For a credit card, it is the stated APR on your statement. Enter it as a percentage, such as 5.0 for 5%.

Compounding Frequency — How many times per year interest is compounded and added to the balance. Banks compound savings accounts daily or monthly. CDs are often monthly or quarterly. Bonds typically pay semi-annually. Choose the frequency that matches your specific account or product.

• Daily (365): most money market and high-yield savings accounts
• Monthly (12): most savings accounts and personal loans
• Quarterly (4): some CDs and bonds
• Semi-annually (2): many corporate and government bonds
• Annually (1): some savings accounts and simple interest products

Principal Amount (optional) — If you enter a deposit amount, the calculator will show exactly how much interest you would earn in one year at the calculated APY. This makes the percentage difference concrete.

What APR and APY actually are

APR (Annual Percentage Rate) is the flat yearly rate before compounding. It is the rate you earn per year if interest is only calculated once, at year end, and never earns additional interest on itself.

APY (Annual Percentage Yield) is the effective yearly rate after compounding is factored in. It represents what you actually earn over a full year because it accounts for interest earning interest throughout the period.

The distinction matters because compounding means your interest earns interest. If a bank pays 5% APR compounded monthly, you earn slightly more than 5% over the full year because each month’s interest payment begins earning its own interest the following month.

APR tells you the rate. APY tells you what the rate actually produces. For savers, APY is the number that matters. For borrowers, APY is the number they should look at instead of the advertised APR, because it represents the true annual cost.

Importantly, APY will always be greater than or equal to APR. They are equal only when compounding happens exactly once per year (annually). Every other compounding frequency produces an APY that exceeds the APR.

The formula

APY = (1 + APR/n)^n − 1

Where:

• APR is the nominal annual rate, expressed as a decimal (so 5% becomes 0.05)
• n is the number of compounding periods per year

The exponent n is what does the compounding work. Raising (1 + r/n) to the power n mathematically captures the effect of reinvesting interest n times per year.

For the five standard frequencies:

Frequency	n	Formula	APY for 5% APR
Annually	1	(1 + 0.05/1)^1 − 1	5.0000%
Semi-annually	2	(1 + 0.05/2)^2 − 1	5.0625%
Quarterly	4	(1 + 0.05/4)^4 − 1	5.0945%
Monthly	12	(1 + 0.05/12)^12 − 1	5.1162%
Daily	365	(1 + 0.05/365)^365 − 1	5.1267%

The continuous compounding limit is APY = e^APR − 1, where e ≈ 2.71828. For 5% APR continuously compounded: APY = e^0.05 − 1 = 5.1271%. Daily compounding gets within 0.0004% of continuous compounding, making it effectively equivalent for any practical purpose.

Why banks advertise different numbers for the same product

US banking regulations require financial institutions to disclose APY prominently on deposit products. This is consumer protection: APY is the more honest number for what you actually earn.

But loan products advertise APR. Credit card statements show APR. Mortgage offers lead with APR. This is because APR is the lower number for borrowers, making the product appear less expensive.

The result is a systematic asymmetry in financial advertising. For anything you put money into (savings, CDs, investments), you will see APY. For anything you borrow (credit cards, mortgages, auto loans), you will see APR.

Smart consumers should ask the opposite question in each case: for savings accounts, ask what the APR (underlying rate) is to understand what you lose if compounding changes. For loans, mentally convert the stated APR to APY to understand the true annual cost.

Real-world impact of compounding frequency

The numbers from the formula may look small: 5% versus 5.116% is only 0.116 percentage points. But the impact accumulates meaningfully over time and on large balances.

$100,000 at 5% APR for 20 years:

Compounding	APY	Final Balance	Difference vs Annual
Annually	5.000%	$265,330	baseline
Semi-annually	5.063%	$268,506	+$3,176
Quarterly	5.094%	$270,113	+$4,783
Monthly	5.116%	$271,264	+$5,934
Daily	5.127%	$271,791	+$6,461

The difference between annual and daily compounding on $100,000 over 20 years is $6,461. That is purely from more frequent application of the same 5% rate. No additional contributions, no higher rate, just compounding frequency.

For institutional investors or people with large savings, this difference scales proportionally. At $1,000,000 for 20 years, the compounding frequency difference exceeds $64,000. This is why banks offering high-yield savings accounts specifically advertise “compounded daily” rather than monthly.

APR to APY conversion examples

High-yield savings account: 4.75% APR, compounded daily

APY = (1 + 0.0475/365)^365 − 1 = 4.864%

If you have $25,000 in this account, you earn $1,216 in year one, not $1,187.50. The compounding adds $28.50 more than the APR alone would suggest.

CD: 5.0% APR, compounded monthly

APY = (1 + 0.05/12)^12 − 1 = 5.116%

A $10,000 six-month CD at these terms earns: $10,000 × ((1 + 0.05/12)^6 − 1) = $253.13 in six months.

Bond: 6.0% APR, compounded semi-annually

APY = (1 + 0.06/2)^2 − 1 = 6.090%

Bonds that pay twice yearly (coupon payments every 6 months) use semi-annual compounding. The effective annual yield is 6.09%, slightly above the stated coupon rate.

Credit card: 22% APR, compounded daily

APY = (1 + 0.22/365)^365 − 1 = 24.60%

If you carry a $5,000 balance on this card for a full year, you pay $1,230 in interest, not $1,100. The extra $130 is the compounding premium that the advertised 22% rate does not reveal.

Converting APY back to APR

Sometimes you need to go the other direction: you have an APY and want the underlying APR. This comes up when comparing products that quote APY with loans that quote APR.

APR = n × [(1 + APY)^(1/n) − 1]

For a savings account with 5.116% APY compounded monthly:

APR = 12 × [(1 + 0.05116)^(1/12) − 1]

= 12 × [(1.05116)^(0.08333) − 1]

= 12 × [1.004167 − 1]

= 12 × 0.004167

= 5.000% APR

This confirms that 5.116% APY with monthly compounding comes from 5.0% APR. The conversion is perfectly reversible.

The bottom line

APR and APY are two ways of expressing the same underlying rate. The conversion formula is simple and the difference is predictable: more frequent compounding produces a higher APY relative to APR.

For savers, APY is the number to focus on. It tells you what your account actually earns. When comparing savings accounts, compare APYs directly.

For borrowers, convert the stated APR to APY to understand the true annual cost, especially for products that compound frequently like credit cards. The gap between APR and APY on a high-interest card can be 2-3 percentage points, which is the difference between 22% and 24.6% on a $10,000 balance, or $260 per year.

The formula is simple enough to run in your head for rough estimates. For precision, use the calculator, especially when evaluating large balances or multiple compounding periods.