APY Calculator
Convert APR to APY. See the true annual yield with compounding effects.
Investment Details
Compounding Comparison
| Frequency | APY | 1-Year Earning |
|---|---|---|
| Yearly | 5.000% | $500.00 |
| Semi-Annually | 5.062% | $506.25 |
| Quarterly | 5.095% | $509.45 |
| Monthly | 5.116% | $511.62 |
| Weekly | 5.125% | $512.46 |
| Daily | 5.127% | $512.67 |
| Continuous | 5.127% | $512.71 |
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APR vs APY: Understanding True Returns
Banks and investment platforms advertise interest rates in two ways: APR (Annual Percentage Rate) and APY (Annual Percentage Yield). The difference? Compounding.
APR is the "simple" rate. APY is what you actually earn after interest compounds on itself. A 5% APR with monthly compounding becomes 5.12% APY—that extra 0.12% is "free" money from compounding.
The APY Formula
APY = (1 + r/n)^n - 1r = nominal rate, n = compounding periods per year
Example: 6% APR, monthly compounding (n=12):
APY = (1 + 0.06/12)^12 - 1 = (1.005)^12 - 1 = 6.168%
On $10,000: Earn $616.80 instead of $600 — extra $16.80 from compounding!
10% APR: Effect of Compounding Frequency
| Frequency | Periods/Year | APY | $10K Earnings |
|---|---|---|---|
| Yearly | 1 | 10.000% | $1,000.00 |
| Quarterly | 4 | 10.381% | $1,038.13 |
| Monthly | 12 | 10.471% | $1,047.13 |
| Daily | 365 | 10.516% | $1,051.56 |
| Continuous | ∞ | 10.517% | $1,051.71 |
Daily vs yearly compounding = $51.56 extra per year on $10K. Over 20 years, this compounds to thousands.
Key Concepts
For Savers
Always compare APY, not APR. Daily compounding beats monthly. Even 0.1% APY difference adds up over years.
For Borrowers
Credit cards quote APR but compound daily—real cost is higher. 20% APR = 21.94% APY. Always check true APY.
Rule of 72
Years to double = 72 ÷ APY. At 6% APY, money doubles in 12 years. At 8% APY, only 9 years.
DeFi Warning
100%+ DeFi APYs include token rewards that depreciate. Real yield is often 10-20% after token value drops.
Calculator Features
Frequently Asked Questions
What is the difference between APR and APY?
APR (Annual Percentage Rate): The 'nominal' or 'stated' rate without compounding. Simple interest on principal only. APY (Annual Percentage Yield): The 'effective' rate including compounding. What you ACTUALLY earn or pay. Example: 5% APR compounded monthly = 5.116% APY. On $10,000: APR gives $500/year, APY gives $511.62/year. The difference: $11.62 extra from compounding. For savings, you want high APY. For loans, you want low APR (though lenders must disclose APY).
How is APY calculated?
Standard formula: APY = (1 + r/n)^n - 1. Where r = nominal annual rate, n = compounding periods per year. Example: 6% APR, monthly compounding. APY = (1 + 0.06/12)^12 - 1 = (1.005)^12 - 1 = 6.168%. Continuous compounding: APY = e^r - 1. For 6% continuous: APY = e^0.06 - 1 = 6.184%. Continuous gives the theoretical maximum APY for any nominal rate.
What is continuous compounding?
Continuous compounding compounds interest infinitely often—every infinitesimal moment. Formula uses Euler's number (e ≈ 2.71828): Future Value = P × e^(r×t). It's the mathematical limit as compounding frequency approaches infinity. Used in: (1) DeFi/crypto protocols (compound every block), (2) Financial derivatives pricing (Black-Scholes), (3) Advanced investment modeling. Practical difference from daily is tiny: 5% continuous = 5.127% APY vs daily = 5.126% APY. Nearly identical for most purposes.
Why does compounding frequency matter?
More frequent = Higher APY. 10% APR comparison: Yearly: 10.000% APY. Semi-annually: 10.250% APY. Quarterly: 10.381% APY. Monthly: 10.471% APY. Daily: 10.516% APY. Continuous: 10.517% APY. On $100,000, the difference between yearly and daily compounding is $516/year. Over 10 years with reinvestment, this compounds further. Always compare APY, not APR, when choosing savings products.
What are typical APYs for different investments?
2024 typical ranges: High-Yield Savings: 4.5-5.5% APY. CDs/Fixed Deposits: 4.5-5.5% APY (varies by term). Money Market: 4-5% APY. Treasury Bills: 4.5-5.5% APY. Government Bonds: 4-5% APY. Corporate Bonds: 5-7% APY (higher risk). Dividend Stocks: 2-4% yield (plus growth). DeFi Stablecoins: 5-15% APY (smart contract risk). DeFi Volatile: 10-100%+ APY (very high risk). Higher APY always means higher risk. Free money doesn't exist.
How does APY work in DeFi (crypto)?
DeFi protocols often show high APYs (10-100%+) because: (1) Auto-compounding: Many compound earnings automatically (Yearn, Beefy). (2) Token rewards: APY includes reward tokens that may drop in value. (3) Variable rates: APY fluctuates based on supply/demand. (4) Impermanent loss: Not factored into displayed APY. (5) Risk premium: Smart contract bugs, rug pulls, regulatory risk. 'Real' APY is often much lower than advertised. A 50% displayed APY might yield 10-20% in stable value after token depreciation.
How do I calculate daily passive income from APY?
Simple approximation: Daily Income = (Principal × APY) ÷ 365. Example: $100,000 at 5% APY. Daily = ($100,000 × 0.05) ÷ 365 = $13.70/day. Monthly = $13.70 × 30 = $411/month. To earn $100/day: Need $100 × 365 ÷ 0.05 = $730,000 at 5% APY. Or $365,000 at 10% APY. Or $182,500 at 20% APY. Higher APY means more risk—balance based on your situation.
Should I prioritize high APY or low risk?
Depends on your situation: Prioritize Safety (low APY) if: Emergency fund, short-term needs, retirement in 5 years, low risk tolerance. Stick to FDIC-insured savings, treasuries. Accept More Risk (higher APY) if: Long time horizon (10+ years), money you can afford to lose, diversified portfolio. Consider CDs, bond funds, dividend stocks. Avoid Extreme APY unless: You understand the specific risks, only using 'play money', have done thorough research. Never put essential savings in 20%+ APY products.
How does APY affect mortgage and loan payments?
For loans, APY tells you the TRUE cost: Credit Card: 20% APR compounded monthly = 21.94% APY. On $5,000 balance = $1,097/year interest, not $1,000. Mortgage: Usually compounds monthly. 6.5% APR ≈ 6.7% APY. Personal Loan: Check if rate is APR or APY—some predatory lenders quote APR but compound daily. Always calculate APY to compare loans fairly. A 10% APR loan compounding daily costs more than 10.5% APR compounding annually.
What is the Rule of 72 and how does it relate to APY?
Rule of 72 estimates doubling time: Years to Double = 72 ÷ APY. Examples: 4% APY: 72 ÷ 4 = 18 years to double. 6% APY: 72 ÷ 6 = 12 years. 8% APY: 72 ÷ 8 = 9 years. 12% APY: 72 ÷ 12 = 6 years. Use APY, not APR, for accurate results. Time is powerful: At 7% APY, your money doubles every ~10 years. In 30 years, it octuples (8× growth).