The difference between APR and APY: For the same 20%, how much difference can compound interest make in the result?

Many people get confused when they see APR and APY on deposits, loans or DeFi product pages: both say percentages, as if they are talking about how much interest they can earn in a year, but why do some platforms list 20% APR and some 20% APY? In fact, these two are not the same thing. APR only looks at simple interest, and APY also takes into account compound interest. Therefore, if the same product compound interest more than once a year, APY must be higher than APR. Let’s use a specific example to make it clear.

Suppose you deposit $10,000 into an account with an annual interest rate of 20%, calculated as simple interest based on APR. Then after 12 months you get $2,000 in interest, and the next year you get another $2,000 based on the original $10,000, which is the same every year. This is simple interest: interest is always calculated only on the original principal.

But if the same $10,000, 20% annual interest product is converted to monthly compounding, the situation is different. The interest is not paid in one lump sum at the end of the year, but is settled every month (12 times a year) and rolled into the principal. The interest you get in the first month is the principal multiplied by the monthly interest rate. The amount is not large, but the key is that it will be added to the principal. Starting from the second month, this interest will also participate in the next round of interest calculation. Over the year, your balance would be about $12,194, $194 more than simple interest. This extra part is the "compound interest" brought by compound interest.

If the interest rate is compounded daily, the annual interest rate of 20% will be settled once a day, 365 times a year. The balance at the end of the year was about $12,213, just a little more than compounded monthly. The difference is very small in one year, but if it extends to several years, the impact of compound interest frequency will become more and more obvious.

So there is a fixed relationship between APR and APY: as long as interest is compounded more than once a year, APY is always equal to or higher than APR. In the case of monthly compound interest, an APR of 20% corresponds to approximately 21.94% APY; in the case of daily compound interest, the same 20% APR corresponds to approximately 22.13% APY. Remember a simple association: there is a "Yield" in APY, which is more complicated and has a higher number; the "Rate" in APR is a simple static interest rate.

In the crypto world, this distinction comes up often. When you go mining, staking or borrowing, the platform may mark it as APR or APY. If both products are marked with APY, don’t forget to look at the compound interest cycle. Assuming that the APR of two products is the same, one is compounded on a daily basis and the other is compounded on a monthly basis, the actual return of the one based on the day will be slightly higher.

In recent years, some new ways of playing DeFi have emerged, such as restaking and liquidity staking derivatives. These products are often marked with APR, but if the rewards are automatically reinvested, or the pledged derivatives themselves will increase in value, the actual income may be different from the APR on the page. Before participating, please confirm that this number does not include all levels of income. The same is true when providing liquidity to a liquidity pool: the pool may charge APY based on daily compound interest, but how much you actually get depends on whether the reward is manual reinvestment or automatic reinvestment by the protocol.

There is another pitfall unique to crypto products: some platforms use “APY” to refer to cryptocurrency rewards instead of fiat currency. Cryptocurrency prices fluctuate greatly, and the rewards may be larger or smaller when converted into fiat currency. For example, if a product offers a 50% APY for a certain token, it may seem tempting, but if the price of that token plummets, converting all your positions into fiat currency may still be lower than the initial investment.

Starting in 2024, U.S. and overseas regulators will tighten their gaze on how crypto platforms advertise their yields. The U.S. SEC has taken action against several platforms because they were misleading when displaying APR and APY, such as marking high annualized returns without clearly explaining compound interest assumptions, token inflation, or related risks. So when you look at the product yourself, be sure to verify: whether the interest rate is annualized, whether compound interest is included, and what kind of assets are used to pay for the rewards. Don’t just read the big words, read the terms.

When comparing two products, the safest way is to use the same indicator. If you know the compounding frequency, you can convert APR to APY. The formula is APY = (1 + APR/n)^n - 1, where n is the number of compounding times per year. Many online calculators now do calculations automatically. If you are too lazy to calculate by hand, at least ask: Is this number simple interest or compound interest? How often is interest compounded?

Higher APY doesn’t necessarily mean better. You also need to consider factors such as the risks of the product itself, liquidity restrictions, and reward currency fluctuations. Two products have the same APY, but the risks may be very different. Don’t just focus on the revenue numbers.

One final reminder: This kind of content is only for popular science and does not constitute investment advice. The income figures may change with the market, so verify it yourself before making a decision.

Reference: Binance Academy Source: https://academy.binance.com/en/articles/apy-vs-apr-what-s-the-difference