APR and APY

When participating in DeFi, two key metrics that you'll often come across are the Annual Percentage Rate (APR) and the Annual Percentage Yield (APY). Both are measures of the return you can expect over a year, but they are calculated differently and can provide different insights.

APR (Annual Percentage Rate)

APR is a straightforward measure of the annual rate of return, without taking compound interest into account. It's calculated by multiplying the rate per period by the number of periods in a year.

For example, if a DeFi pool gives a reward rate of 0.5% per day, the APR would be:

0.5% * 365 = 182.5%

This means that if you put your money in the pool and leave it there for a year, without reinvesting the rewards, you would earn 182.5% of your initial investment.

APY (Annual Percentage Yield)

APY, on the other hand, takes compound interest into account. It assumes that the rewards you earn are reinvested back into the pool, which then earn rewards of their own. This can lead to significantly higher returns over time.

The formula for APY is:

APY = (1 + r/n)^(nt) - 1

where:

• r is the interest rate (in decimal form, so 5% would be 0.05)

• n is the number of compounding periods per year

• t is the number of years

In the context of DeFi, the compounding period is often daily. So if a pool or farm gives a reward rate of 0.5% per day (or 0.005 in decimal form), the APY would be:

APY = (1 + 0.005/1)^(1*365) - 1 = 2023.89%

This means that if you put your money in and reinvest the rewards every day, you would earn 2023.89% of your initial investment in a year.

Differences Between APR and APY

The main difference between APR and APY is that APR does not take compound interest into account, while APY does. This means that APY will always be equal to or higher than APR.

In the context of DeFi, whether APR or APY is more relevant depends on how often you plan to reinvest your rewards. If you plan to reinvest frequently (e.g., daily), then APY will give a more accurate picture of your potential returns. If you don't plan to reinvest, or will only do so infrequently, then APR may be more relevant.

It's also worth noting that the actual APR and APY you achieve can depend on various factors, such as changes in the price of the tokens in the pool, changes in the reward rate, and transaction fees for reinvesting rewards. Therefore, it's always important to do your own research and understand the risks involved.