Convert between Annual Percentage Rate (APR) and Annual Percentage Yield (APY). Compare how different compounding frequencies affect your effective returns and understand the true cost of borrowing or earning.
Your credit card charges an APR of 18% compounded daily. The APY is calculated as: (1 + 0.18/365)^365 - 1 = 19.72%. This means you're effectively paying 19.72% annually, not 18%, due to daily compounding.
A high-yield savings account offers an APY of 4.5% compounded monthly. The equivalent APR is: 12 × ((1 + 0.045)^(1/12) - 1) = 4.41%. The bank quotes the APY because it's higher and more attractive to savers.
When compounding is annual (n=1), APR and APY are equal. A loan with 6% APR compounded annually has an APY of exactly 6%. This is why simpler products like some mortgages still use annual compounding.
With continuous compounding, APY = e^APR - 1. For a 10% APR compounded continuously: e^0.10 - 1 = 10.52%. Continuous compounding produces the highest effective yield for any given APR.
At 0% interest, APR = APY = 0 regardless of compounding frequency. No compounding can create interest from zero, confirming the formulas are consistent at the boundary.
APY = Annual Percentage Yield (effective annual rate)
APR = Annual Percentage Rate (nominal rate)
n = Number of compounding periods per year
Continuous: APY = eAPR - 1
APR = Annual Percentage Rate (nominal rate)
APY = Annual Percentage Yield (effective annual rate)
n = Number of compounding periods per year
Continuous: APR = ln(1 + APY)
Step 1: Select the conversion direction — APR to APY (for loans) or APY to APR (for savings accounts).
Step 2: Enter the rate as a percentage.
Step 3: Choose the compounding frequency that matches your product.
Step 4: Click "Calculate" to see the converted rate, the difference, and a comparison table showing how the effective rate changes with different compounding frequencies.
APR (Annual Percentage Rate) is the nominal interest rate that lenders advertise for loans and credit cards. It represents the simple annual rate before compounding is factored in. APR is what you'll see on mortgage documents, auto loans, and credit card statements.
APY (Annual Percentage Yield) is the effective annual rate that accounts for the effects of compounding. Compounding occurs when interest is earned on previously earned interest, causing your balance to grow faster than simple interest would suggest. APY is what banks advertise for savings accounts, CDs, and investment products.
The key relationship: APY is always ≥ APR when compounding occurs more than once per year. The two are equal only when compounding is annual (n=1) or when the rate is zero. This difference matters tremendously over time — a credit card with 18% APR compounded daily has an effective rate of 19.72% APY.
⚠️ Important: When comparing financial products, always compare the same metric — APY to APY for savings and investments, APR to APR for loans. Mixing them can lead to inaccurate comparisons and poor financial decisions.
The frequency of compounding directly impacts the effective yield you earn or pay. More frequent compounding results in a higher effective rate for the same nominal rate. Here's how different frequencies compare for a 5% APR:
| Compounding | Periods/Year | APY for 5% APR | Extra Yield |
|---|---|---|---|
| Annual | 1 | 5.000% | 0.000% |
| Semi-Annual | 2 | 5.063% | 0.063% |
| Quarterly | 4 | 5.095% | 0.095% |
| Monthly | 12 | 5.116% | 0.116% |
| Daily | 365 | 5.127% | 0.127% |
| Continuous | ∞ | 5.127% | 0.127% |
Notice that the biggest jump occurs between annual and semi-annual compounding, while the difference between daily and continuous compounding is negligible. This diminishing marginal benefit is important to understand — daily compounding is only slightly better than monthly for most practical purposes.
For high-rate products like credit cards (15-25% APR), the difference between APR and APY becomes significant. A 24% APR compounded daily yields 27.11% APY — that's over 3% more in effective interest. For low-rate products like mortgages (3-6% APR), the difference is smaller but still meaningful over a 30-year term.
Understanding the difference between APR and APY is crucial for making smart financial decisions. Here are practical tips for applying this knowledge:
When taking out a loan, always ask for the APR and check the compounding frequency. A lower APR with daily compounding could cost more than a slightly higher APR with annual compounding. Credit card companies typically use daily compounding, which maximizes their interest income. Use this calculator to find the true annual cost by converting APR to APY.
Banks advertise APY because it's higher and more attractive. When comparing savings accounts, CDs, or money market accounts, look at the APY rather than the nominal rate. However, be aware of introductory rates that expire, minimum balance requirements, and fees that can reduce your effective yield.
For quick estimates: the difference between APR and APY is approximately (APR² × n) / (2n²) for small rates, but the exact formula is always preferred. Use this calculator to get precise numbers for any rate and compounding scenario.