June 8, 2023

# APR vs. APY: Linear & Exponential Interest

APR and APY are two common metrics displayed by decentralized applications, but what do they mean?

In the world of DeFi, the abbreviations “APR” and “APY” are like salt and pepper. Incredibly common, and yet, very different! Becoming familiar with these terms is vital to being a successful DeFi enthusiast!

## What is APR?

APR stands for “annual percentage rate”, to put simply, it is a metric that indicates the potential return on investment after a single year. For example, an APR of 100% means that you would double your initial investment within a year’s time. If you put in \$20 into a yield farm that is paying out 100% APR, in a year you would have another \$20 in your pocket, for a total of \$40!

It is critical to understand two things about APR:

1. APR is a linear metric.
2. APR is a snapshot.

Consider the above example with the MANUAL CRYSTL Pool, where a user may deposit \$CRYSTL tokens to earn more \$CRYSTL tokens. According to the APR displayed on this Pool, a user would receive a return of 183.01% on their \$CRYSTL investment within one year.

Let’s say you purchased \$100 worth of \$CRYSTL today and staked them in the Pool. If you were to leave this \$100 investment in the Pool and come back in one year, \$183.01 would be available for you to claim from the Pool in \$CRYSTL rewards (according to the displayed APR metric).

Every day, you would be accumulating about \$0.5013 worth of \$CRYSTL, computed as follows: 183.01% / 365 * \$100 = ~\$0.5013. In other words, APR is a linear metric, and assumes that returns are exactly the same, day to day.

Adding up these rewards with your initial \$100, you would have a total of \$283.01 worth of \$CRYSTL at a return of 183.01%. However, this is only true if the price of \$CRYSTL, as well as a variety of other parameters remained completely stagnant for the entirety of the year. This is where it is important to recognize that APR is a snapshot, an approximated calculation based on a variety of factors available at this precise moment in time.

## What is APY?

APY on the other hand, stands for “annual percentage yield”. Like APR, APY is a metric that describes the potential return on investment after a single year. However, there is something special that distinguishes APY from APR and that is the fact that APY takes compounding interest into account. Again, like in the previous example an APY of 100% means that you would double your initial investment. If you put in \$20 into a yield farm that is paying out 100% APY, in a year you would have another \$20 in your pocket, for a total of \$40! If you are confused and wondering where is the difference, don’t worry – we will explain!

It is critical to understand two things about APY:

1. APY is an exponential metric.
2. APY is a snapshot.

Consider the above example with the AUTO CRYSTL Pool, where a user may deposit \$CRYSTL tokens to earn more \$CRYSTL tokens. According to the APY displayed on this Pool, a user would receive a return of 520.61% on their \$CRYSTL investment within one year.

Let’s say you purchased \$100 worth of \$CRYSTL today and staked them in the Pool. If you were to leave this \$100 investment in the Pool and come back in one year, you would find that your balance has become a whopping \$620.61 (according to the displayed APY metric)! How is such an enormous difference possible between the MANUAL and AUTO CRYSTL Pools? The answer is simple, compounding interest!

Unlike the MANUAL CRYSTL Pool, the AUTO CRYSTL Pool automatically compounds earnings daily. In other words, APY is an exponential metric that takes into account the effects of continuously reinvesting earned rewards.

On Day 1, you start with \$100 and earn ~\$0.50, and add it back to earn more.

On Day 2, you have \$100.50, earn ~\$0.504, and add it back to earn more.

On Day 3, you have \$101.01, earn ~\$0.506, and add it back to earn more.

On Day 365, you have \$617.51, earn ~\$3.096, and add it back to earn more!

As you can see, compounding interest yields exponential results as your earnings are continuously added to your existing balance. In the above example the compounding was computed daily – but in practice, many blockchain protocols actually perform compounding multiple times a day. Higher compounding frequencies result in even higher APYs!

It is important to remember that just like APR, APY is also a snapshot, which means it is based on the parameters present at the time the APY is observed and does not take into account changes in price or fluctuations in the underlying interest rate throughout the compounding period of a year.

## Auto-Compounding Vaults

The idea of APYs is highly relevant to the auto-compounding Vaults implemented by Crystl Finance. Behind the scenes, a Vault is actually built on top of a farm contract that accepts liquidity provider tokens (LP) and pays out APR rewards (linear)! However, what’s magical about Vaults is that they are programmed to automatically reinvest the underlying farm’s earnings into more LP – effectively turning the APR rewards into APY rewards (exponential).

Not only does this mean exponentially higher returns for investors, but it brings enormous benefits to project owners as Vaults lead to exponential growth on token liquidity and support the price growth for the underlying assets with positive buy pressure as half of the farmed tokens are used to purchase each of the tokens in the LP pair (one of which is of course, the token of the project).

Below you can see some example values of Farm APRs and their potential APYs with a Vault implementation. The APYs were computed assuming hourly compounding frequency (24 times a day).

As a project owner, choosing between having a Farm or a Vault to incentivize liquidity providers for your token should be a no-brainer!

• ❌ With a Farm, many liquidity providers will sell off their rewards into other tokens instead of the token of your project.
• ✅ With a Vault, liquidity providers will enjoy high exponential interest on their investment while supporting your token with consistent & automated, positive buy pressure.
• ❌ With a Farm that becomes saturated with TVL, it is harder to retain attractive APR figures.
• ✅ With a Vault, even if the is underlying Farm is saturated with TVL, APY figures may remain attractive!
• ❌ With a Farm, liquidity IS NOT “sticky” and lacks psychological comfort, many providers choose to disband liquidity when they observe that the LP value isn’t growing.
• ✅ With a Vault, liquidity IS “sticky“! Providers monitor their LP growth and are comforted by its ever increasing value, both in terms of LP tokens and their equivalent \$USD representation.

The following graphic provides some estimations of buy pressure which may be achieved with Crystl Vaults through annual buybacks for the project token. For instance, a farm that sustains a 75% APR would result in a 111.69% APY with a Vault implementation that has an hourly compound frequency. If the Vault has an initial 10K TVL in the liquidity pair, then this would result in an annual buyback of \$5.3K on the project token! On the other hand if the initial Vault TVL is 50K, the annual buyback figure is 26.5K!

Finally, for the last example – if the initial Vault TVL is 100K, the annual buyback results in as much as \$53.0K of buy pressure on the project token. Similar examples are outlined for other hypothetical Farm APRs and their respective Vault APYs. Of course, with higher APRs, the exponential returns become extremely prominent.

If you are interested in a Vault implementation for your project, please fill out the following form or contact the Crystl Finance Lead of Business Development on Telegram: @Crypto_Gummy_Bear

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