apy apr calculator

What Is the Difference Between APY and APR?

APY (Annual Percentage Yield) and APR (Annual Percentage Rate) are both annualized interest rates, but they are not the same thing. APR is the stated yearly rate before the impact of compounding, while APY includes compounding. Because of that, APY is usually higher than APR when interest is compounded more than once per year.

If you are saving or investing, APY tells you what you can actually earn over a year. If you are borrowing, APR helps you compare quoted loan rates, but you should still check fees and payment structure for total cost.

How This APY APR Calculator Works

APR to APY Formula

For standard periodic compounding: APY = (1 + APR / n)ⁿ - 1

• APR is in decimal form (5% = 0.05)
• n is compounding periods per year (12 for monthly, 365 for daily, etc.)

For continuous compounding: APY = e^APR - 1

APY to APR Formula

Rearranging the equation for periodic compounding: APR = n × [(1 + APY)^1/n - 1]

For continuous compounding: APR = ln(1 + APY)

Why Compounding Frequency Matters

The more frequently interest compounds, the larger the gap between APR and APY. This is why two accounts with the same APR can have slightly different APYs depending on whether they compound monthly, daily, or continuously.

• Annual compounding: very small APR/APY gap
• Monthly compounding: moderate gap
• Daily compounding: slightly higher APY
• Continuous compounding: theoretical upper bound

How to Use the Calculator

1. Select your conversion direction: APR to APY or APY to APR.
2. Enter the known rate in percent.
3. Choose your compounding frequency.
4. Optionally add starting balance and years to project growth.
5. Click Calculate to view converted rates and projection.

Example: APR to APY

Suppose a savings account advertises a 6.00% APR with monthly compounding. The effective APY is:

APY = (1 + 0.06/12)¹² - 1 = 0.061678...

So your APY is about 6.1678%. If you started with $10,000 and left it for one year, your ending balance would be approximately $10,616.78.

Common APY vs APR Mistakes

• Comparing APR from one product to APY from another (not apples-to-apples).
• Ignoring compounding frequency entirely.
• Assuming loan APR includes all fees (it often does not include every possible charge).
• For savings, focusing only on nominal rate rather than effective annual return.

APY and APR in Real Life

Savings Accounts and CDs

Banks often show APY prominently for deposit products because APY reflects what you can earn over a year with compounding. This makes product comparisons easier.

Credit Cards and Loans

Borrowing products are usually quoted in APR terms. For short-term balances or revolving debt, understanding monthly and daily periodic rates can have a major impact on total repayment cost.

Bottom Line

Use APR to understand the quoted nominal rate. Use APY to understand the true annual effect of compounding. A quick APY APR conversion helps you compare offers accurately, estimate growth, and make better financial decisions. Keep this calculator handy whenever you evaluate savings accounts, certificates of deposit, money market funds, or borrowing options.