When choosing a savings deposit in a bank or a deposit in cryptocurrency, users are often interested in such indicators as APY and APR. They reflect the profitability of investments and allow comparing different offers of storing financial assets. But there is a significant difference between APY and APR, which is important to understand in order to make the right investment decisions.
In this article, we will go into detail about what APY and APR mean, what the fundamental difference between them is, as well as look at specific examples of calculating interest using APY and APR on deposits in banks and crypto platforms.
This knowledge will help you intelligently choose profitable deposit products and get the maximum income from your investments.
What lies behind the numbers: understand the essence of APR
Once we have decided on the choice of deposit or deposit, we are interested in the key indicator — the expected annualized return on our funds. To display it, financial companies use APR (Annual Percentage Rate).
APR is the annual interest rate that a bank or crypto platform promises to customers on their deposits. For example, with an APR of 10% on an annual deposit of $1,000,000, you will receive 1,000,000 + 10% of 1,000,000, that is, $1,100,000.
However, in practice, the real income may differ from the stated APR rate. The whole point is that the standard APR does not take into account the effect of compound interest, which is used by most banks and crypto companies.
Unlike simple interest, where the amount of accruals depends only on the initial deposit amount, compound interest means receiving interest on interest. That is, the interest accrued for one period (month, quarter), itself begins to bring income in subsequent periods.
Let’s say you invested $10,000 in a deposit for 5 years at 7% annual percentage rate (APR) with monthly capitalization of interest.
At simple interest for the 1st month, you will earn 7%/12 = 0.58% of $10,000, which is $58. For the whole year you will earn 12*58 = $696 regardless of the previous months.
And with compound interest, the deposit amount will increase each month by the interest earned. In the 2nd month you will already receive 0.58% not from 10,000, but from $10,058. In the 3rd month — from $10,117, etc. In a year, the total income will be $735 instead of $696.
After 5 years, the difference will reach $1,500 in your favor. This is the effect of compound interest, which is not accounted for in the APR.
As you can see from the example, due to the effect of compound interest, the real return on a deposit or deposit over the long term can significantly exceed the APR that was originally promised by the financial company.
To take into account the effect of compound interest and to understand how much you can really earn on a deposit, another important indicator is used — APY. Unlike APR, it reflects the total income taking into account the reinvestment of interest on interest.
Let’s understand in detail what APY is and how to use it to calculate the real income from fixed-rate deposit products.
APY formula: what it is and how it works
Unlike the static APR, APY allows you to accurately calculate the real return on a deposit or deposit.
APY (Annual Percentage Yield) is a measure of the annual return on a financial product, taking into account the effect of compound interest.
APY reflects the total amount of money you will receive at the end of the deposit term if you reinvest the interest accrued for each period. The APY also automatically includes the frequency of interest accrual (monthly, quarterly, etc.).
The formula for calculating APY is as follows:
APY = (1 + APR/n)^n - 1
Where: «n» is the number of interest accrual periods per year.
Let’s return to the example from the previous section. You opened a deposit for 5 years at 7% per annum with monthly interest payments. Let’s find the real income on this deposit:
(1+0.07/12)^12 - 1 = 0.0735 or 7.35%
Now let’s find the total amount of the deposit by the end of the term at a given APY. The formula used is:
P * (1 + APY)^n
Where: «P» is the initial deposit amount and n is the deposit term
So, over 5 years at an APY rate of 7.35% you will earn:
10,000 * (1 + 0.0735)^5 = $12,367
That is, the real income is higher than the stated APR rate and will amount to $2,367.
Unlike APR, the value of which is fixed for the entire term, APY is dynamic: it takes into account the capitalization of interest for each period and therefore changes from the initial forecast to the actual income received.
APR and APY: nuances of interest rate comparison
From the example above, you can see that with compound interest, the real income from a deposit or deposit over time can significantly exceed the original APR rate.
When comparing the yields of different financial products, it’s critical to use one metric — either APR or APY. Otherwise, you run the risk of comparing values that are not comparable.
For example, deposit A with an APR of 10% is not necessarily better than deposit B with an APR of 7%. After all, deposit B may have a higher APY due to monthly interest capitalization.
To correctly compare deposits/deposits, you can use online calculators where you can quickly convert rates by the desired frequency of interest accrual. This is especially useful when analyzing crypto deposits and staking.
In addition, the frequency of interest accrual should be considered for comparison. For example, if one product offers an APY of 12% monthly and another offers 10% daily, the second product may be more favorable due to the higher frequency of interest capitalization. With daily capitalization, the interest-on-interest effect is 365 times more frequent. Accordingly, the deposit amount grows faster and the real yield is higher than at the same rate but with monthly capitalization.
It is also essential to understand exactly how interest is accrued in a particular crypto product. In some cases, APY may refer to the reward received in cryptocurrency rather than the actual income after its conversion into fiat. Accordingly, when digital coin rates fluctuate dramatically, returns may decrease despite the steady growth of cryptocurrency rewards. To fully understand the risks, it is important to study the terms and interest accrual mechanisms of a particular product.
It is important to realize that annual percentage yield (APY) is a more complex metric than APR because it takes into account the effect of reinvesting interest. Due to the accrual of income on income, APY is always higher than APR, unless the interest accrual is strictly once a year.
Therefore, when choosing financial products, it is extremely important to study the mechanics of income accrual in detail in order to correctly interpret the APY and APR values and calculate the real expected return taking into account all the nuances.
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