APR vs APY: What’s the difference and how to calculate it

APR vs APY

APR stands for Annual Percentage Rate.

‍Let’s say you take out a loan or want to choose a credit card. Some credit card companies will offer lower APR than others. Put simply, APR gives an estimate of all the costs that come with borrowing money. In that regard, it is different from the simple interest on the loan. Because there will also be fees and costs to obtain the loan. So, if you’re deciding between multiple loans or credit cards, APR will give you a better idea of the actual cost you will pay for borrowing money.

For example, if you were to take out a loan of €10.000 and the APR is 10%, you will pay a total amount of €1.000 in interest over that first year.  

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However, what you really want to look at is the APY. APY stands for Annual Percentage Yield.

The big difference between APR and APY is that the latter takes compound interest into account.

Let’s dive into that a little more. 

What is compound interest?

Compound interest was called ‘mankind’s greatest invention’ by none other than Albert Einstein. This is where things get interesting. To put it simply, compound interest is the interest you receive upon the initial interest, which was added to the original deposit or loan. Making money with money. It makes sense that when you receive interest on your investment, the total amount of money will grow. 

Recommended: What is compound interest and how does it work?

APR vs APY simple comparison

So, now you know a bit more about APR vs APY. When you want to take on a loan, for example when deciding on a mortgage to buy a house, it’s important to keep both these numbers in mind. Banks will often tell you about the APR and boast about low rates to lure you in. 

But what they often don’t disclose is the intra-year compounding of the loan. And that could result in you paying more than you originally would have thought because you haven’t taken the compound interest of the loan into consideration. And the more frequently the bank compounds your loan, the higher the APY will be and the higher your interest will become over the years. If you know the APY beforehand, you will have a better idea of what you will actually end up paying. 

Understanding APR vs APY with an Example

Let’s understand this with an example we used before. You want to borrow €10.000 and you can choose between two lenders. We’ll call them Lender A and Lender B. 

Lender A offers an APR of 9.4%. The loan is compounded yearly. This means that the amount of interest you will actually pay per year is 9.4% of the entire loan, which is €940.  

Lender B offers a lower APR of only 9%. But the catch is that the loan is compounded daily. That means that the amount of interest you will actually pay per year is 9.42%. In this example, that means you will pay more than you would pay €942 in interest over the first year. That’s more than you would with lender B, even though the APR was lower. 

This tells you that although APR is important, it’s also very important to keep compounding interest in mind because it can make a big difference. Especially when taking out a big loan for a long period of time, such as 20 to 30 years for a mortgage. 

APR vs APY in crypto

APR vs APY in crypto follows the same rules as within other investments. To create compound interest in crypto, investors can engage in interest-earning activities such as storing crypto in savings accounts, depositing tokens, and yielding to agriculture. This provides liquidity to liquidity pools. You can engage in interest-earning activities like these by using cryptocurrency exchanges, wallet applications, and decentralized finance protocols (DeFi).  

APR vs APY calculator

Calculating APR is pretty straightforward. When you know the interest rate (for example 10%) and the initial amount (for example €10.000), then you just multiply them: €10.000 x 0,10= €1.000. As you see, the amount of interest you will have to pay yearly is €1.000.

Things get a little bit more complicated when you wish to calculate the APY. Here’s how to calculate APY:

APY = (1 + r/n )ⁿ – 1

r = interest rate

n = the number of times per year that the interest is compounded

Let’s see how this works with our previous example of a €10.000 investment with a 10% interest rate that is compounded weekly. In this case, r = 0.10 and n = 52, because there are 52 weeks in a year, so this interest is compounded 52 times per year. To put it in the formula, would look something like this:

[1 + (0.10 /52)]⁵² – 1 = 0.10506479

To turn this number into a percentage, you simply multiply it by 100% and you get 10.51%

This means that in this example, your annual percentage yield will be 10.51%. Given the initial investment of €10.000, this comes down to 10.000 x 0.1051 = €1051 that you will earn in interest. 

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Disclaimer:

This blog is for educational purposes only. The information we offer does not constitute investment advice. Please always do your own research before investing. Any views expressed in this blog and by BOTS do not constitute a recommendation that any particular cryptocurrency (or cryptocurrency token/asset/index), portfolio of cryptocurrencies, transaction, or investment strategy is suitable for any specific person.

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