DeFined: APR vs. APY

A visual comparison between the ROI of APR vs. APY.

Short Answer

APR (Annual Percentage Rate) indicates an annual rate of return based on your original investment. APY (Annual Percentage Yield) reflects an annual return that compounds your interest, which maximizes return on investment.

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In this article, we explore the ideas behind three financial fundamentals: interest, APR, APY. We’ll understand how they impact lending and borrowing, learn how to calculate them, and apply that context to Decentralized Finance (DeFi).

All investors understand the desire to find a higher APR or APY yield, or return, on their investments. The search for investment opportunities or strategies that offer high returns in the safest, fastest way has attracted many private investors, hedge funds, venture capitalists, and average consumers to the cryptocurrency industry and, more specifically Decentralized Finance (DeFi).

Unfortunately, though, the multi-chain DeFi landscape can come with a steep learning curve: the barriers to entry are rather high, the terminology is complex and varied, and many of the most profitable strategies require constant monitoring and movement of tokens to give investors high yields.

One noticeable grievance held by investors of all experience levels and wallet sizes is that the language around APR and APY is convoluted in the DeFi space.

While APR / APY is used across DeFi to represent return on investment (ROI) for liquidity pools, yield farming, staking, loans and lending, there can be some discrepancies as to how DeFi platforms are reporting this data. Some show interest in APR, while other projects show APY — and many are using native tokens to boost or support claims for both.

Let’s look at what each term means in the context of DeFi and what you, the DeFi investor, can look for to understand how teams use this language as they offer their product to you.

What is Interest?

Put simply, interest is the additional fee for borrowing money, or the reward for loaning assets.

Banks earn interest from borrowers through products like mortgages, personal or business loans, car loans, or credit cards. Investors earn interest by depositing assets into a bank, who then lends the assets to other customers.

Decentralized Finance (DeFi) offers various opportunities for investors to earn interest or additional returns through, for example, the project’s lending, liquidity pools, staking, and yield farming offerings. DeFi platforms range in offering, capability, security, and rewards APR/APY so it’s important for all investors to understand and research a DeFi protocol before making any investment decisions.

How are Interest Rates Determined?

Interest rates are determined by a number of factors. In the United States, for example, the Federal Reserve — more specifically, the Federal Open Markets Committee (FOMC) — considers various macroeconomic influences and makes decisions that influence how central banks adjust and offer their own rates.

In traditional finance, banks and lenders combine various factors like a person’s credit score, payment history, and other personal information to determine the rate to offer on a loan.

In DeFi, however, the playing field is significantly more level: investors have access to the same offered rates because there’s no background check, no credit score, no payment history and no centralized authority to make decisions.

How to Calculate Simple Interest

Understanding and calculating interest is easiest among our three topics. This is because APR and APY take other elements, like fees or compounded interest, into account.

To properly calculate simple interest, a borrower or lender needs to know: the principal amount, the interest rate, and the length of the terms. We can visualize the equation like this:

I = PxRxT

Where, in our formula:

  • I equals interest
  • P equals the principle amount
  • R equals the interest rate
  • T equals the time / length of terms

Typically, we refer to time in units of years.

A visual outline of a simple interest calculation formula.

A simple example of calculating interest:

Let’s say Satoshi invests $10,000 into a savings account, or (even better!) a DeFi lending platform. The interest rate is 5% and their funds will be locked in for one full year (12 months).

How much interest will Satoshi make? What will Satoshi hold after the period is over?

Our Formula: Interest = Principal x Rate x Time
Our Formula with Figures: Interest = 10,000 (dollars) x 0.05 (5%) x 1 (year)
Our Math: 10,000 x 0.05 x 1 = $500

  • Satoshi’s simple interest would earn them $500.
  • After the one year period, Satoshi would have $10,500.

While rates like 5% are often found in DeFi, a traditional bank offering 5% interest is unheard of. This is part of the reason decentralized finance has gained traction among more tech-savvy investors.

Understanding simple interest is only part of the equation, however. Other elements like fees or compounding impact the affects of interest for both lenders and borrowers. This is reflected more clearly via APR and APY metrics, which we’ll cover below.

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What is APR?

In the context of investing, APR (Annual Percentage Rate) indicates an annual rate of return — the yearly amount you’ll be paid in interest — for your original investment. APR is generally the term used for the context of borrowing and loans, whereas APY is often used for lending and investing.

In the context of lending and borrowing, APR reflects the amount of interest a borrower would be required to pay on a loan over a given year. It’s the cost for the borrower to take out the loan.

A visual graphic of APR (Annual Percentage Rate)

A simple example:

  • After a year, a $10,000 investment with a 10% APR will return the investor $1,000, giving them a total of $11,000.
  • After the second year, an $11,000 investment with a 10% APR will return the investor $1,100, giving them a total of $12,100.
  • After the third year, a $12,100 investment with a 10% APR will return the investor $1,210, giving them a total of $13,310.

Since APR only takes the principal investment into account, it is not as profitable as APY, as we’ll see below. Be careful to read the terms associated with any investment. Investors may incur fees for early withdrawal, transfers, or other activity that could impact the final result.

This may sound very similar to the interest rate, but there are some differences. In the context of more traditional finance like housing mortgages, APR terms includes fees and additional expenses like closing costs, broker fees, etc. while simple interest rate does not. APR generally offers a broader, more strategically clear outline of total costs for borrowing. APR can included a fixed or variable rate depending on the lender’s terms of the loan.

How to Calculate APR

To properly calculate APR, a borrower needs to know: the principal (amount borrowed), the interest rate, the fees and costs for the loan, and the number of days in the terms.

A popular formula for calculating APR can be shown as:

APR = ((F + I / P / N) x 365) x 100

Where, in our formula:

  • F equals the fees and charges from the lender
  • I equals the interest rate on the loan
  • P equals the principal borrowed
  • N equals the number of days in the loan terms

Which simply translates to:

APR = ((Fees, Charges + Interest / Principal / N) x 365) x 100

A visual outline of an Annual Percentage Rate calculation formula.

Let’s assume we take a small loan over the course of two years. Let’s say the loan is $10,000. Recall that APR includes the interest and any applicable fees.

  • Let’s assume the interest on the loan is 5%.
  • Let’s assume that other / additional charges is $150.

First, let’s confirm the interest rate. $10,000 at 5% = $500 x 2 years (730 days) = $1,000

Then, based on our formula above, our calculation would look like:

APR = ((150 + 1,000 / 10,000 / 730) x 365) x 100

  • First, we — 1,150 / 10,000 = 0.115
  • Then, we — 0.115 / 730 = 0.00015753…
  • Next, we — 0.00015753 x 365 = 0.05749…
  • Finally, we — 0.0575 x 100 = 5.75

Our last step simply converts the decimal to a percentage value. (0.0575 = 5.75%)

Based on the operations above, we can see that our APR for a $10,000 loan over a two year period is 5.75%.

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Regarding APR, Keep In Mind:

Banks and lenders may differ in the ways they calculate APR. Borrowers should always take time to read supplied materials and documents and do their own research before borrowing.

APR does not take into account the complexities of compounding interest. This can impact the amount the borrower has to pay back over time, depending on the life of the loan.

The rate at which APR is applied (charged) to the borrower may vary. This can impact the amount owed by the borrower.

Rates can be fixed or varied (“variable”) depending on the lender’s terms. Variable APR is influenced by factors like the prime rate, a decision that US banks and lenders make and is influenced, in part, by the Federal Reserve — more specifically, the Federal Open Markets Committee (FOMC).

Borrowers should take care to read all terms provided by the lender. APR may increase after a promotional period, if a borrower misses a payment, etc.

  • Lenders or credit card companies my offer an “introductory APR” that offers borrowers better terms for a short period.
  • Lenders may incur fees if they withdraw their funds before the end of the terms. Associated fees may significantly impact the interest on a loan.

What is APY?

APY (Annual Percentage Yield) reflects an annual rate of return — the yearly amount you’ll be paid in interest — for your original investment and regularly compounded interest. APY is generally the term used for lending and investing, whereas APR is often used for the context of borrowing.

The frequency at which the interest is compounded changes based on the platform or organization. Compounding can be monthly, weekly, daily — it’s entirely up to the platform the investor chooses to interact with. The faster the compounding, the higher the return over time.

Think of APY like a snowball rolling down a mountain. As the snowball (original investment) rolls down the hill (time), more snow accumulates (interest) and the snowball becomes exponentially larger (compounding).

A more frequent rate of compounded interest amplifies the difference between the APR and APY.

If the snowball rotates at a faster rate down the hill, it naturally would gather more snow and grow larger, faster. We can think of compounding interest in the same way.

A visual graphic of APY (Annual Percentage Yield)

This same impact can be applied to borrowing, too. Borrowers with credit cards, personal loans, mortgages, etc. that have interest will also experience the compounding effect of their debts. It’s important that borrowers be mindful of this when considering loans and the impact on their finances over the long term.

How to Calculate APY

To properly calculate APY, a borrower needs to know: the period rate and the number of compounding periods based on the terms.

A popular formula for calculating APY can be shown as:

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

Where, in our formula:

  • r equals the periodic interest rate
  • n equals the number of compounding periods

The component that creates such a distinction between APR and APY is the “n” value in APY’s formula, as this reflects the frequency of compounding interest. The higher the frequency of compounding, the larger the difference between APR and APY.

A visual outline of an Annual Percentage Yield calculation formula.

Let’s assume we have a savings account with $10,000 that earns an annual interest of 5%. This means we’ll earn $500 after a year, totaling $10,500.

Let’s look at how much we’ll earn if our interest compounds every month. We can do this by updating our formula:

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

APY = 1 + 0.05/12)12-1 = 0.051162…
Convert 0.051162 to percentage (x100) = 5.1162%
Multiply the principal by APY% to determine result: $10,000 x 5.1162% = $511.62

At the end of the 12 month period, your $10,000 investment would now be worth $10,511.62 — the compounding impact of APY would earn an additional $11.62.

This may seem like a small instance, but this can have dramatic effects for investors over longer periods of time.

How Might This Look in DeFi?

Let’s assume our friend Satoshi invests 10 Bitcoin (BTC) into a DeFi platform. The APY for Bitcoin lending is a whopping 20%. Satoshi decides to leave his 10 BTC in the platform for a full year.

Let’s assume the DeFi platform compounds every month; 12 times a year. During each recalculation, the interest is added to the original investment amount and the subsequent month period builds on the prior’s sum.

Based on our APY calculation, Satoshi’s formula for 10 BTC looks like:

10 Bitcoin x 1 year x 12 rebalancing periods (months).

APY = (1 + 0.20/12)12-1

  • Step A: (1 + 0.016667)12-1
  • Step B: (1.016667)12-1
  • Step C: 1.21939588252-1
  • Result = 0.21939588252

Multiply x 100 to get Percentage (%) = 21.939%

10 x 21.939% = 10 x 0.21939 = 2.1939

Satoshi’s starting Bitcoin = 10 BTC
After a full year, Satoshi will have earned = 2.1939 BTC
Satoshi’s final Bitcoin balance = 12.1939 BTC

APY earnings (2.1939) vs. APR earnings (2).

How to Consider Choosing DeFi Products

We cannot stress enough the importance of doing as much research as possible before moving funds into a DeFi protocol and interacting with their smart contract(s).

There are many factors at play, but a few basic thoughts to keep in mind when determining if a DeFi platform is right for you include:

  1. their fees (and clarity)
  2. their community
  3. their team
  4. their contracts/code
  5. their reputation
  6. their APR / APY rates
  7. their documentation

An Important Note for DeFi Investors

While a DeFi project may show APY, the user may be responsible for gathering and reinvesting the rewards (interest) back into the protocol. Meaning, the effort of compounding may fall on the DeFi investor. Always be sure to research DeFi projects to truly understand the inner workings before interacting with the platform.

Many DeFi products to not automatically reinvest interest/rewards, which is why auto-compounding services like, Beefy Finance, Autofarm, or Reaper Farm, are quite popular. These products will handle the reinvesting/compounding for you for a small fee. This saves DeFi users and investors a great deal of time. It’s worth noting, however, that using additional projects ads a layer of security risk due since there are more smart contracts being used on a regular basis.

A visual comparison between the ROI of APR vs. APY.

There can be a frustrating lack of clarity in DeFi with regards to APR and APY listings. They can be – and sometimes are – incorrect or misleading. Regularly, the APR or APY will include that DeFi protocol’s native token as part of the rewards.

This can be misleading for a number of reasons. One reason is that it can mislead investors into expecting returns higher than what they receive. Second it’s not always clear to the investors that some of the APY includes the protocol’s token, which may be of no interest to the investor and may indeed have very little value at all. Investors should take the time to understand if a DeFi product is incorporating native tokens or fiat value as the standard of return in their offering.

Worse, however, is the occurrences where some DeFi platforms use APR and APY interchangeably, which is — as we’ve learned — simply inaccurate. Understanding the principals of, and mathematics behind, interest, APR, and APY can help lenders, borrowers, and investors have more clarity in their financial experience.

No matter the platform, investors and users in both traditional and decentralized finance products must take care to understand the details and terms of any investment.

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