In this article, we will review the equivalent rate calculator. This simple tool is designed to convert an interest rate between two different compound frequencies. At the same time, it ensures that the effective interest rate is unchanged. That can be used for investment products or savings accounts so that the interest is compounded twice or several times a year.
The equivalent interest rate is employed by a variety of financial calculators. They all work on the principle of setting diverse payment and compounding frequencies. For example, this applies to the loan calculator, interest rate calculator, and amortization calculator. We recommend that you have all of these tools in your arsenal of financial calculators.
Here, we are going to focus on the equivalent interest rate calculator. You will learn how to employ this tool when computing the equivalent rate. In addition, you will learn how to calculate it by hand using the proper formula. That’s not all. You can also find out more about AER (annual equivalent rate) if you read through the article. It is worth reading!
What Is the Equivalent Interest Rate?
The interest rate is the cost of borrowing money. It is the amount of money that a borrower pays to a lender in order to use the lender’s money. The interest rate is usually expressed as an annual percentage or as a percentage of the amount that is being borrowed.
Interest rates are often quoted as a nominal rate plus an inflation rate, which is called the real interest rate. The real interest rates are always lower than nominal rates because of inflation. This is one of the most important factors in determining how much it will cost for someone to borrow money for a certain period of time.
The higher the interest rate, the more expensive it will be for someone to borrow money and vice versa. It is calculated by dividing the total amount of money owed by the total number of payments, then multiplying by 100%. For example, if you borrow $100 for five years and make 12 payments, your interest rate would be 5%.
When it comes to the annual equivalent interest rate, it is the actual interest rate savings, loans, or investments are going to yield upon compounding. If there are two or more compounding periods per year, the nominal or stated rate will be lower than this value.
Annual Equivalent Rate (AER) – What Is It?
When talking about the effective rate, we actually think of the annual equivalent rate (AER). The annual equivalent rate is also known as the APY (annual percentage yield) or effective annual interest rate. It’s the interest rate on financial products or loans that are received by restating the nominal interest rate. If compounding occurs yearly, then you need to express it as the equivalent interest rate.
For different compound frequencies, AER is different. Take a look at the table below to see the value of the equivalent rates for corresponding nominal annual rates at various compounding frequencies.
| Nominal Interest Rate (%) | Semi-Annually (%) | Quarterly (%) | Monthly (%) | Weekly (%) | Daily (%) |
| 1 | 1.0025 | 1.0038 | 1.0046 | 1.0049 | 1.0050 |
| 5 | 5.0625 | 5.0945 | 5.1162 | 5.1246 | 5.1267 |
| 10 | 10.2500 | 10.3813 | 10.4713 | 10.5065 | 10.5156 |
| 15 | 15.5625 | 15.8650 | 16.0755 | 16.1583 | 16.1798 |
| 20 | 21.0000 | 21.5506 | 21.9391 | 22.0934 | 22.1336 |
| 25 | 26.5625 | 27.4429 | 28.0732 | 28.3256 | 28.3916 |
AER Cons & Pros
Let’s check the main advantages and disadvantages of the annual equivalent rate. One of the best advantages of the annual equivalent rate is that the rate of interest is real in contrast to the Annual Percentage Rate (APR). This makes a difference. That’s because the AER takes into account compounding effects.
Furthermore, the annual equivalent rate is very useful for investors, as it makes it easier for them to evaluate loans, bonds. It also helps them estimate the real ROI (return on investment). The AER plays a crucial role in discovering the accurate ROI when it comes to interest-bearing assets.
However, the AER isn’t stated when estimating various investment options, so investors have to calculate it on their own. Another disadvantage of the annual equivalent rate is that fees (associated with selling or purchasing the investment) are not included in this computation.
How to Use the AER?
While the AER can be used for different purposes, its application comes down to comparing investments and loans. Let’s see how it works.
- Using the annual equivalent rate to compare investments: The AER comes in handy when deciding between two investments or CDs (certificates of deposit). Simply check the stated interest rates for each of them to determine which investment option is better.
- Using the annual equivalent rate to compare loans: It can help you compare the amount of interest if you have a loan or credit card debt. If the stated interest rates are the same while the compound frequency is different, you will be able to choose the better loan option after calculating the AER. The same goes for credit cards.
ER Formula: How to Calculate the Equivalent Rate
Now that you know more about the equivalent rate, it’s time to see how it is calculated. Use the following formula:
ER = (1+ r/n) ^ n – 1
Where:
- r is the stated interest rate
- n is the number of compounding periods (it tells you how many times compounding is performed per year)
This means you will only need two values (r and n) when calculating the equivalent rate. We will take an example to help you understand how it works. For instance, if there are 3 compounding periods a year and the interest rate is 4.00%, the equivalent rate (ER) will be as follows:
ER = (1 + 0.04/3) ^3 – 1
ER = 1.01333^3 – 1
ER = 0.00334
In this example, the equivalent rate is 0.00334. Since the ER is usually displayed as a percentage, it is equal to 0.034%. This computation is slightly difficult and it takes time. That’s why you should use the ER calculator. With this handy tool, you will be able to calculate the equivalent rate quickly and accurately. It is worth using!