What Is the Difference Between APR and APY?

What Is the Difference Between APR and APY?

In the world of crypto and decentralized finance, you will encounter two closely related but meaningfully different metrics everywhere: APR (Annual Percentage Rate) and APY (Annual Percentage Yield). Understanding the distinction between these two numbers is crucial for accurately evaluating yield opportunities, comparing lending rates, and knowing what your investments are truly earning.

The short version: APR is the simple interest rate, and APY is the rate after accounting for compounding. But the implications of this difference are more significant than many newcomers realize, especially at higher rates and longer time horizons.

Defining APR

APR, or Annual Percentage Rate, represents the raw interest rate for a year without factoring in the effect of compounding. It is a straightforward, linear calculation of what you would earn (or pay) if interest were only calculated once at the end of the year.

APR in Simple Terms

If you deposit 10,000 USDC at a 12% APR, you would earn exactly 1,200 USDC in interest over one year, assuming simple interest (no compounding). Your total would be 11,200 USDC.

APR is commonly used in contexts where:

• Rewards must be manually claimed and reinvested
• The protocol does not automatically compound returns
• You want to express the base rate before compounding

Where You See APR in Crypto

APR is commonly displayed in:

• Yield farming platforms where you manually harvest and reinvest rewards
• Staking dashboards where rewards accrue separately and must be restaked
• Some DEX liquidity pool interfaces
• Borrowing rate displays on certain protocols

Defining APY

APY, or Annual Percentage Yield, represents the total effective return over one year including the effect of compound interest. It accounts for the fact that as you earn interest, that interest itself starts earning interest, creating an exponential growth effect.

APY in Simple Terms

Using the same 10,000 USDC at a 12% rate, but now compounded monthly: each month you earn 1% (12% / 12 months) on your growing balance. After month one, you have 10,100 USDC. In month two, you earn 1% on 10,100 USDC (101 USDC), not just on the original 10,000.

After a full year of monthly compounding, you would have approximately 11,268 USDC — that is a 12.68% APY from a 12% APR. The extra 68 USDC came purely from compounding.

Where You See APY in Crypto

APY is commonly displayed in:

• Lending protocols where interest auto-compounds (Aave, Compound)
• Auto-compounding vault strategies (Yearn, Beefy)
• Staking interfaces that auto-restake rewards
• Savings products and interest-bearing accounts

The Mathematics Behind the Conversion

Understanding how to convert between APR and APY helps you compare opportunities accurately.

Converting APR to APY

APY = (1 + APR/n)^n - 1

Where n is the number of compounding periods per year.

Let us calculate APY from a 10% APR at different compounding frequencies:

• Annual (n=1): APY = (1 + 0.10/1)^1 - 1 = 10.00%
• Semi-annual (n=2): APY = (1 + 0.10/2)^2 - 1 = 10.25%
• Quarterly (n=4): APY = (1 + 0.10/4)^4 - 1 = 10.38%
• Monthly (n=12): APY = (1 + 0.10/12)^12 - 1 = 10.47%
• Daily (n=365): APY = (1 + 0.10/365)^365 - 1 = 10.52%
• Continuous: APY = e^0.10 - 1 = 10.52%

Notice how the difference between daily and continuous compounding is negligible. In DeFi, where interest compounds every block (roughly every 12 seconds on Ethereum), the compounding is effectively continuous.

Converting APY to APR

APR = n x ((1 + APY)^(1/n) - 1)

For continuous compounding:

APR = ln(1 + APY)

Where ln is the natural logarithm.

When the Difference Is Small vs Large

At low interest rates, the difference between APR and APY is minimal. At 2% APR with daily compounding, the APY is approximately 2.02% — barely noticeable. But at higher rates, the gap widens significantly:

• 5% APR → 5.13% APY (daily compounding)
• 20% APR → 22.13% APY
• 50% APR → 64.87% APY
• 100% APR → 171.83% APY
• 1000% APR → 2,198,690% APY

This exponential relationship is why extremely high "APY" numbers in DeFi can look astronomical while the underlying APR is (relatively) more modest. A protocol advertising 1000% APY sounds incredible, but the underlying APR is "only" about 240% — which is still very high and likely unsustainable, but not as extreme as the headline number suggests.

APR vs APY for Lenders

If you are lending crypto to earn yield, the distinction between APR and APY affects how you evaluate and compare opportunities.

Auto-Compounding Lending Protocols

On protocols like Aave and Compound, your lending interest compounds automatically. When you deposit USDC, you receive aUSDC or cUSDC tokens whose value increases over time as interest accrues. You do not need to manually claim and reinvest. For these protocols, APY is the most accurate representation of what you will earn.

If Aave shows a supply APY of 5.13%, you know that includes compounding. If you convert that to APR, it is roughly 5.0% — the base rate before compounding.

Manual Compounding Scenarios

Some yield opportunities do not auto-compound. For example, many yield farming protocols distribute reward tokens that sit in your wallet until you manually sell and reinvest them. In these cases, APR is what you actually earn unless you take the extra step of compounding yourself.

Your actual APY depends on how often you reinvest:

• Reinvest once a year → APY equals APR
• Reinvest monthly → slightly higher effective APY
• Reinvest daily → APY approaches the theoretical maximum

But gas costs for reinvesting can eat into returns, especially on Ethereum mainnet. There is an optimal compounding frequency where the benefit of more frequent compounding just outweighs the gas cost of the reinvestment transaction.

Understanding Lending Yield Displays

When evaluating where to lend, such as comparing rates surfaced by aggregators, always check whether the displayed rate is APR or APY. A protocol showing 6.0% APR and another showing 6.0% APY are not offering the same return — the APR protocol is effectively offering slightly less because it does not include compounding. Understanding how lending yield works helps you contextualize these numbers within the broader mechanics of supply and demand.

APR vs APY for Borrowers

For borrowers, the APR vs APY distinction affects how much you actually pay for a loan.

Borrowing Costs in DeFi

When you borrow on a DeFi protocol, the interest on your loan compounds just like the interest earned by lenders. If a protocol shows a borrow APR of 8%, your actual cost over a year will be slightly higher (approximately 8.33% with daily compounding) because the interest compounds on your debt.

When comparing borrowing rates on platforms like Borrow by Sats Terminal, which aggregates rates across protocols like Aave, Compound, and Morpho, make sure you are comparing consistent metrics. A 7% borrow APY on one protocol might be cheaper than a 6.5% borrow APY on another protocol depending on fee structures and other factors.

Why Borrowers Should Care About Compounding

For short-term loans (days or weeks), the difference between APR and APY is negligible. But for longer-term borrowing positions, compounding interest can add up significantly:

On a 100,000 USDC loan at 10% APR:

• After 1 month: ~833 USDC interest (APR and APY nearly identical)
• After 6 months: ~5,000 USDC at APR vs ~5,127 USDC at equivalent APY
• After 1 year: 10,000 USDC at APR vs 10,517 USDC at equivalent APY

The longer you hold the position, the more the compounding effect costs you as a borrower.

APR vs APY for Stakers

Staking rewards are another area where APR and APY semantics matter.

Native Staking

When you stake tokens directly (e.g., running an Ethereum validator), rewards accrue but do not automatically compound. Your staked ETH earns rewards, but those rewards sit separately until you exit and restake or until protocol-level changes enable auto-compounding. In this case, the staking rate is most accurately described as APR.

Liquid Staking

Liquid staking tokens like stETH (Lido) work differently. The value of stETH increases relative to ETH as staking rewards accrue, effectively auto-compounding. If Lido displays a staking APR of 3.5%, the effective APY for stETH holders is slightly higher (approximately 3.56%) because of this automatic compounding mechanism.

Auto-Compounding Vaults

Platforms like Yearn Finance or Beefy Finance offer vaults that automatically compound staking or farming rewards. These vaults typically display APY because they handle the reinvestment process for you, often at optimal intervals to maximize returns while minimizing gas costs.

Practical Tips for Comparing Rates

Here are guidelines for making accurate comparisons:

Normalize to One Metric

Always convert rates to the same metric before comparing. If Protocol A shows 8% APY and Protocol B shows 7.8% APR, convert Protocol B's APR to APY (approximately 8.11% with daily compounding) to see that Protocol B actually offers a slightly better return.

Factor in Compounding Behavior

Ask yourself whether the yield auto-compounds or if you need to manually reinvest. If manual reinvestment is needed, the displayed APR may be more realistic than a theoretical APY calculation, especially after accounting for gas costs.

Consider the Full Picture

APR and APY are just one dimension of evaluating a yield opportunity. Also consider:

• Protocol risk: How well audited and battle-tested is the platform?
• Asset risk: Are you exposed to price volatility?
• Liquidity risk: Can you withdraw when you need to?
• Rate stability: How much does the rate fluctuate over time?
• Fees: Are there deposit, withdrawal, or performance fees?

Watch for Misleading Displays

Some protocols show extremely high APY figures that are technically correct but practically misleading. A yield farming pool might advertise 500% APY, but this figure assumes you compound your rewards optimally and that the reward token price remains constant — both of which are unlikely. The underlying APR might be a more useful number for setting expectations.

Real-World Scenarios

Let us look at a few practical scenarios that illustrate why the APR/APY distinction matters.

Scenario 1: Choosing Between Two Lending Protocols

Protocol A offers 6.2% APY on USDC lending with auto-compounding. Protocol B offers 6.0% APR on USDC lending, also with auto-compounding. Which is better?

Convert Protocol B's 6.0% APR to APY: approximately 6.18% with daily compounding. Protocol A's 6.2% APY is slightly better, but the difference is small (0.02%). At this point, other factors like protocol risk and liquidity become more important differentiators.

Scenario 2: Evaluating a Farming Opportunity

A new yield farm offers 80% APR in its governance token. The auto-compounding vault shows this as 122% APY. Your actual return depends on:

• Whether you use the auto-compounding vault (APY) or compound manually (something between APR and APY)
• Whether the governance token maintains its current price
• Whether the APR remains constant (it almost certainly will decrease as more capital enters)

In practice, you would likely earn somewhere between the APR and APY figures, with the actual result heavily influenced by token price movements and rate changes.

Scenario 3: Comparing Borrowing Costs

You want to borrow 50,000 USDC against your Bitcoin holdings. Borrow by Sats Terminal shows you rates across multiple protocols.

Borrow normalizes APR and APY side-by-side for every supported lender and shows the resulting LTV and liquidation price next to each one. So in this scenario you'd see Protocol A and Protocol B converted to the same basis before approving anything. Protocol A offers 7.5% borrow APR and Protocol B offers 7.8% borrow APY.

Converting Protocol A to APY: approximately 7.79% with daily compounding. The two protocols are nearly identical in cost. In this case, you would look at other factors like collateral requirements, liquidation parameters, and user experience to make your decision.

Summary

The difference between APR and APY comes down to compounding. APR is the simple annual rate, while APY includes the effect of earning returns on your returns. In DeFi, where compounding can happen thousands of times per year, this distinction is mathematically significant, especially at higher rates.

For practical decision-making: use APY when comparing auto-compounding opportunities, APR when rewards require manual reinvestment, and always normalize to the same metric before comparing across protocols. Most importantly, look beyond the headline rate to understand the source of yield, the associated risks, and the sustainability of the returns being offered.

Understanding this fundamental distinction is a building block for navigating the broader world of crypto yield and making informed decisions about where to deploy your capital, whether you are lending for yield or borrowing against your assets.