What is AER?

To choose the best way for saving money, a person must check deposit offers from bank institutions. And here comes the Annual Equivalent Rate which affects directly the money earned over a year. To get familiar with the term, understand the calculation process deeply, and be able to select a good deposit agreement, we introduce you to this Genome article.

What does AER stand for?

The AER stands for the Annual Equivalent Rate. In the financial world, the AER represents the interest rate that a depositor receives for a fixed deposit sum over a year or on a yearly basis. For a deep understanding of the Annual Equivalent Rate, we must first briefly explain two other financial concepts: the interest and the compounding.

The interest is the payment that a depositor receives from the financial institution. The payment is calculated of the amount above the repayment of the original deposit sum. The rate of interest then is equal to the interest sum paid over a certain period divided by the original deposit sum.

The compound interest though is the interest a depositor receives on interest. In other words, it is a sum received interest together with the original deposit sum with the result of the reinvesting interest. So the interest in the upcoming period will be received on the original deposit sum plus the previously accumulated interests.

Both interest and compound interest are something each of us having the deposit deals with every day. Surely definitions do sound pretty confusing, but we better make it simpler with an example.

Let’s imagine Sam, he is an ordinary guy, just like me or you. Sam has a bank account and it has been a while since he thought about setting up a deposit account to get some bonuses over his savings.

So he plans to deposit 1000 euros with the interest of 5%. So over the first year, he’ll receive on the deposit account 1050 euros. But over the second year, he will have 1102.5 euros. Not only did he receive 50 euros on the initial 1000 euros deposit, but he also received 2.5 euros on the 50 euros in interest. This is what compound interest is: to earn on interest.

What is interesting about compounding is that even 25 cents may grow into hundreds. It does not sound like much at first, but it definitely adds up over time. In 10 years with 25 cents alone on the deposit Sam would have more than 162 euros because of the power of compound interest. And in 25 years he would obtain almost 340 euros. Just with a 25 cents deposit.

And now going back to the Annual Equivalent Rate. What are AER and its interest? The AER is directly related to the interest and compound interest. It shows what the interest rate on the deposit would be if the interest was paid for the entire year and compounded as well. The interest here is calculated to set the amount the depositor receives by adding the interest payment to the original deposit sum. The next interest payment will be based on the marginally higher deposit balance.

No worries, we are about to bring you another example to explain what does AER mean. 

Annual Equivalent Rate formula

The Annual Equivalent Rate formula is [(1 + r/n)^n] – 1

Where r = gross rate interest

And n = number of times interest is paid during a year

How to calculate AER?

To calculate the Annual Equivalent Rate we need to take into consideration the amount of gross interest received in a year [r] that usually is presented in percentage and must be converted to a number, and a number of times the interest is paid annually [n].

The AER calculator:

1. We take the gross interest rate that is paid over the year [r];
2. We divide the gross interest rate by the number of times the interest is paid out during the year [n];
3. We add 1 to this;
4. Then we rise the total to the number of times the interest is paid out during the year [n];
5. And at last, we subtract 1.

The result should be displayed in percentage.

So here is an example of how to calculate the AER rate. Remember our Sam? He found three banks that offered him different percentages [r] and different paid-off periods [n] of the Annual Equivalent Rate. 

Green Bank offers AER at 5% and pays interest on an annual basis. Blue Bank offers AER at 5% as well but pays interest quarterly. And Yellow Bank offers 3% of the Annual Equivalent Rate paying interest monthly.

Green Bank	Blue Bank	Yellow Bank
r = 0.05 (as 5%)n = 1 (as once a year)AER = [1 + (0.05 / 1]^1 – 1AER = 0.05	r = 0.05 (as 5%)n = 4 (as 4 times a year)AER = [1 + (0.05 / 4]^4 – 1AER = 0.0501	r = 0.03 (as 3%)n = 12 (as 12 times a year)AER = [1 + (0.03 / 12]^12 – 1AER = 0.0303
AER is 5%	AER is 5.01%	AER is 3.03%

In the case when the interest is paid more than once during a year the interest is calculated by summing every of the interest payments with the original deposit sum. In the case when the interest is paid quarterly the Annual Equivalent Rate will be higher. The reason for this is that the gross rate would also include interest paid on the interest itself. The Annual Equivalent Rate ignores all the exceptional bonus interests.

How is AER used?

The Annual Equivalent Rate is used to compare the interest rates for deposits between different bank institutions and with different compounding periods, like weekly interest, monthly interest, semi-annual interest, or yearly interest. It also can be used by the person searching for the best saving bank account or an investor reviewing bond yields.

What do you need to know about the annual equivalent rate (AER)

The interest rate AER is paid out under the financial agreement the depositor signed with the bank. The Annual Equivalent Rate allows the depositor to calculate out what the total interest in a year the depositor would receive.

The Annual Equivalent Rate can be compounded:

• Semi-annually
• Quarterly 
• Monthly
• Weekly 
• Daily 

Depending on the compounding period the whole Annual Equivalent Rate might differ after a year-long period. Annual Equivalent Rate can be calculated in the right way only if the depositor knows the frequency of the interest payment. 

Every interest rate determined as an Annual Equivalent Rate will only be applicable in that case when a person does not withdraw money from the deposit account during the year. The Annual Equivalent Rate illustrates what the interest would be if it was paid and compounded yearly. And so any withdrawals from the deposit account would affect the amount a depositor will receive at the end of the year.

What is the difference between AER and APR?

AER or Annual Equivalent Rate is often confused with APR which is Annual Percentage Rate. Well, the Annual Equivalent Rate is calculated on the interest rate on the deposit, Annual Percentage Rate is calculated on the borrowings that a person does for the loan or mortgage, and so on. Annual Equivalent Rate helps depositors to compare various types of financial offers and institutions that are available on the market. One more big difference between AER and APR is that the Annual Percentage Rate does not factorize in compounding interests.

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FAQ

What does AER interest mean?

AER means Annual Equivalent Rate, it shows the interest rate that a depositor will get for a fixed deposit sum over a year or on a yearly basis. Annual Equivalent Rate is directly related to the concept of interest and compound interest. AER represents what the interest rate on the deposit would be if the interest to be paid for the entire year and compounded on top of it. 

How does AER work?

AER has a specific formula. To calculate the Annual Equivalent Rate the one must have two essential numbers: gross rate interest, and the number of times interest is paid during a year. After the gross interest rate that is paid over the year is divided by the number of times the interest is paid out during the year; then 1 is added; then the total is raised to the number of times the interest is paid out during the year; and after 1 is subtracted. The result is displayed in percentage. 

What does 1.5% AER mean?

An annual Equivalent Rate of 1.5% means that the depositor will receive a fixed deposit sum of 1.5% of the interest rate after a year. For example, if the deposit is 100 euros, with AER 1.5%, the depositor will have on the bank account 101.5 euros after one year. But this result is valid only if the number of times interest is paid during a year equals 1, so if the interest is paid annually. In the case when the interest is paid quarterly, monthly or weekly, the Annual Equivalent Rate will be higher.

What does 1% AER mean?

An annual Equivalent Rate of 1% means that the depositor will get a fixed deposit sum of 1% of the interest rate after a whole year. For example, with a deposit of 100 euros, and AER equal to 1%, the person will get 101 euros in their savings account at the end of the year. Again this result is valid only if the number of times interest is paid during a year equals 1, or when the interest is paid once a year. When the interest is paid more often, the Annual Equivalent Rate will be higher.