APR represents the annual interest rate (Annual Percentage Rate), and APY represents Annual Percentage Yield. In the crypto field, APR is generally used in lending scenarios. It represents the amount of interest that will be charged/paid when you lend/borrow. APY is more commonly used in situations such as income farming or providing liquidity, and represents the income you will receive.

It is worth noting that although APR and APY both refer to interest rates, they are measured and calculated differently: APR only takes into account simple interest, while APY also takes into account compound interest.

Let us explain with an example. Let’s say you deposit $1 worth of cryptocurrency, the APR is 5%, and interest is paid at the end of the year. This means that at the end of the year, you will have earned $0.05 in interest and your total balance will be 1 * (1+5%) = $1.05.

Under the same conditions, the APY is 5% at this time. Let’s first assume that interest is compounded only once a year. Based on the calculation formula of APY: total income = (1 + (APY/n))^n (n is the number of compound interest per year), your total balance at the end of the year will be (1 + (5%/1) )^1 = $1.05, which is no different from the APR calculation.

If it is assumed that the interest is compounded once every six months, that is, the interest is compounded once a year. This means that at the end of the first year, not only will you earn interest on your initial deposit, the interest earned in the first half of the year will continue to accrue interest in the second half of the year. At this point, your total balance at the end of the year will be (1 + (5%/2))^2 = $1.0506, which is slightly more than what you would have earned with an APR of 5% high.

What happens if compound interest is compounded more times? Now let's assume that interest is compounded daily, that is, 365 times a year. Your total balance will now be (1 + (5%/365))^365 = $1.0513, which is a higher profit than before.

As a result, the compounding effect of APY can lead to higher returns compared to APR, especially for long-term investments. As the number of compound interest increases over time, the difference between APR and APY will become larger and larger.