In This Article
When making investment decisions, it is important to properly measure the magnitude of potential returns. In staking, farming and lending there are two concepts related to the calculation of probable earnings - annualised interest rate and annualised interest yield. These are different terms, each of which in its own way affects the calculation of earnings in cryptocurrencies.
What is APY
APY in cryptocurrency (Annual Percentage Yield) is an annual percentage yield that takes into account compound interest and shows the real return on investment.
Interest can be accrued at the end of the term, monthly, quarterly or weekly. And with each type of payment, the investor will have a different return on the same amount of investment. APY in cryptocurrency and other financial instruments implies that interest is accrued at certain intervals and then reinvested. This means that for the next term a larger capital is deposited - the initial amount plus the interest already received.
In traditional finance we are familiar with this concept under the name "capitalization" in bank deposits.
An important point: The more frequently interest is paid, the higher the yield. That is, if the amount earned is accrued every day, the investor will eventually receive a higher return compared to, for example, a monthly payment.
How to Calculate APY
The APY percentage is calculated using the formula:
APY = (1 + k/m) ^ (m×t) - 1
k is the interest rate as a decimal fraction,
m is the number of interest accrual periods per year,
t is the number of years.
Example
Michael wanted to invest 1,000 ETH in staking with a rate of 15% for one year, assuming monthly reinvestment of income. Then the real interest would be (1 + 0.15/12) ^ (12×1) - 1 = 0.16. So APY = 16%. This is 1% more than the nominal percentage of 15%. So at the end of the year Michael will earn 160 ETH, not 150 ETH..
Let's look at the Pros and Cons of APY:
What is APR
APR in cryptocurrency (Annual Percentage Rate) is an annual interest rate by which investors calculate potential annual returns.
It is a fixed rate that is independent of other conditions. The yield remains unchanged and does not take into account the effect of compound interest. This method is used by investors more often, as it quickly gives a basic potential of investments without lengthy calculations.
Important point: APR is not convenient for all cryptocurrency products, as it will not show the correct size of possible income for investments with reinvestment
How to calculate APR
A simple formula is used to calculate APR:
APR = (r/n) × 100
r is the amount of interest paid or received,
n is the amount of the loan or deposit.
Example
Let's say Michael decided to take a loan in cryptocurrency on fixed terms: you borrow 50 ETH, pay back 60 ETH after a year. So, the interest overpayment will be 60 - 50 = 10 ETH. Substitute the values into the formula APR = (10/50) * 100% = 20%. That would be the loan rate.
If the borrower knows the APR, but needs to calculate the final payment, another formula can be used:
V = [ n × (1 + APR × t) ]
V is the final payment,
n is the loan amount,
t is the time in years.
Then in Michael's situation the final payment would be: 50 × (1 + 0,2 × 1) = 60 ETH.
To better understand APR, let's break down the strengths and weaknesses of this indicator:
What is the difference between APR and APY
APR and APY are key metrics that are used to calculate the percentage of return on financial transactions. They are used both in the traditional sphere and in the cryptocurrency market. When calculating the probable annual return on the same investment, the user gets different values for these two metrics because they use a different approach.
Let's calculate APR and APY for several similar situations:
1. Invest 15 BTC at 6% for one year, interest accrues every month
APR = 6%, the investor will receive a one-time payment at the end of the year, which will be:
15 × (1 + 0.06 × 1) = 15.9 BTC
APY = (1 + 0.06/12) ^ (12 × 1) - 1 = 0.0617 = 6.17%
so the investor will receive 15 × 1.0617 = 15.9255 BTC at the end of the year. Given the bitcoin exchange rate, the difference of 0.0255 BTC will be significant
2. Invest 15 BTC at 3% for one year with daily interest accrual
APR = 3%, at the end of the year the investor will receive
15 × (1 + 0.03 × 1) = 15.45 BTC
APY = (1 + 0.03/365) ^ (365 × 1) -1 = 0.0305 = 3.05%
As a result, the investor will receive 15 × (1+0. 0305) = 15.4575 BTC
3. Frozen 350 tokens for 2 years at 15% APR with quarterly interest accrual
APR = 15% (30% for 2 years), after two years the investor will receive the frozen coins and reward, which totals to
350 × (1 + 0.15 × 2) = 455 tokens
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APY = (1 + 0.15/4) ^ (4 × 2) -1 = 0.3425 = 34.25%.
As a result, after unfreezing the coins, the investor will be charged 350 * (1 + 0.3425) = 469.875 tokens (APY already takes into account that the interest accrues for two years, so this factor is not taken into account when calculating the final payment)
Practical Examples of APR and APY
The easiest way to calculate potential earnings from APY is to use an online compounding calculator. Suppose you were to consider the effects of monthly compounding as APY does.
Important points that an investor should consider when comparing APR and APY:
- Reinvestment period. First of all, the real interest rate and the frequency of interest payments affect the final income. An APR that accrues once per year will be less than an APY with monthly or other regular accrual with all other things being equal.
- Type of financial product. Although APY is usually higher than APR, it is not always favourable to the user. If a person wants to borrow in cryptocurrency, high rates will be unattractive for him, so it is better to look for APR.
- Service conditions. If an investor chooses between several offers with different parameters, one product calculates APR and the other APY, it is better to bring the final income to one indicator. Otherwise it will not be possible to compare two offers correctly.
- Special instruments. You don't have to puzzle over the formulas yourself. For a more accurate and convenient calculation you can use online services offered by exchanges and DeFi platforms.
Borrower's and Saver's Perspectives
From the Borrower's Viewpoint: As a borrower, your goal is to find the lowest rate possible, aiming to minimize the cost of borrowing money.
From the Saver's Viewpoint: If you're lending money, essentially what you do when you deposit money in a bank or invest — it’s important to seek the highest interest rate available and take advantage of frequently compounded interest. For instance, if you're looking for a high-yield savings account, this is what you should consider.
