A Brief Overview of the Compound Interest Rate Formula
Compound interest is a wonderful thing. For those of you who don’t know, compound interest is when a bank pays interest on your principal, or the original amount of money, plus the interest your account has already earned.
In simpler terms, this means that your interest is capable of earning you even more interest. If you have opened an account that earns compound interest, you could gain hundreds, if not thousands of dollars, that you may not have expected. To find out exactly how much additional money you can earn, however, requires a compound interest formula.
A compound interest formula will be important for keeping track of your current and future finances. If you are debating about future investments or how much money you can put toward a car or house, the compound interest rate formula will give you a good sense of exactly how far your bank account can take you.
Our goal throughout this article, as the title suggests, is to tell you everything you need to know about the compound interest rate formula. While the formula for compound interest may seem complicated, you can master it quickly and use it to your advantage.
We will answer several of the most commonly asked questions regarding the compound formula including the following:
- How do I calculate the compound interest formula?
- Why is the compound interest rate formula important for me to know?
- Is it possible to use a quarterly compound interest formula to more accurately understand my earnings?
We will begin by analyzing the different parts of the formula for compound interest so you know what information you need to use it. We will then move on to real world examples for using the compound interest formula while also discussing why it will benefit you to use it.
If you are already gaining compound interest, you are in luck. While the formula for calculating compound interest may seem intimidating at first, the results will always show how much more money you are making.
How to Make Sense of the Compound Interest Rate Formula
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The formula for calculating compound interest is as follows:
A = P (1 + r/n) (nt)
At first glance, the formula for compound interest probably doesn’t mean much to you. In fact, it may bring back nightmares of high school algebra.
When we break it down, however, it will all make sense. We will begin by going over what each variable of the compound interest calculation formula means.
- A = The amount of money you will have accumulated after n years, including interest. You can also think of this as the answer to the formula for compound interest. It will show you how much value your investment or loan will have in the future.
- P = The principal investment, or the amount of money you initially invested before you began to accumulate compound interest. It will be essential to the accuracy of the compound interest formula that you know exactly how much you invested at the start.
- r = The annual interest rate. You will enter this information into the compound interest rate formula as a decimal.
- n = The number of times interest is compounded, or added to your account, per year.
- t = The number of years you have invested the money for.
If you think about it, using the formula for compound interest is simply a mechanical operation. As long as you have the correct information, the formula to calculate compound interest will give you the right answer every time. You will no longer have to guess how much money you are earning.
In this particular version of the compound interest rate formula, your answer, or A, is the future value of the loan. This includes the compound interest plus the principal. If you simply want to calculate the compound interest, however, you can rework the formula to look like this:
Total compounded interest = P (1 + r/n) (nt) – P
All of the variables in this compound interest formula will be the same as the ones mentioned above. Essentially, you are seeing how much money you will have in the future and then subtracting how much money you invested, leaving you with the amount you will have earned.
Remember that the formula to calculate compound interest will help you see how much money your investment will gain. At the same time, it will help you assess how high your principal investment should be as well as how long you should invest the money. We will discuss these potential benefits of the compound formula after we give an example of how to use it.
An Example of the Compound Interest Formula
Before we discuss the benefits of using the formula for compound interest to assess your investments, we will offer an example for calculating how much money you can earn.
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Let us say that your initial deposit, or principal, is $7,000, and the annual interest rate, compounded monthly, is 4.5%. Also say that you will invest it for a total of 6 years.
Using our simple and compound interest formula, P is $7,000 and r is 4.5/100, or 0.045 when using it as a decimal. Since your interest is compounded monthly, your n, in this case, will be 12 (the number of times it is compounded). Finally, your t is 6, and the A is what you are using the compound interest calculation formula to determine.
When using the compound interest rate formula, remember the rules of PEMDAS, in which everything inside of the parentheses is calculated first. Your current compound interest formula looks like this:
A = 7,000 (1 + 0.045/12) ^ (12(6))
Now that the numbers have been accurately plugged into the compound interest rate formula, we can calculate the numbers inside the parentheses. Multiplying and dividing always come before adding and subtracting, so your new simple and compound interest formula will be:
A = 7,000 (1 + 0.00375) ^ (72)
Then, you can add the one in the compound interest formula’s first parenthesis.
A = 7,000 (1.00375) ^ (72)
Once everything inside the parentheses has been taken care of, you will calculate the exponent, or the E in PEMDAS. This will give you the following compound interest calculation formula:
A = 7,000 x 1.3093
After that, you simply multiply the two numbers together and your A in the compound interest rate formula is $9,165.10.
Now your job is to interpret the results that the formula for compound interest has given you. Keep in mind that our answer, A, is the amount of money that you will have accumulated, including interest. With this in mind, a $7,000 initial investment with an interest rate of 4.5% will become $9,165.10 after 6 years of monthly compounded interest.
Remember that you can then use the compound formula to calculate your total compounded interest. Simply take A and subtract P. Since the initial investment was $7,000, the total compounded interest over 6 years would be $2,165.10.
The compounded interest that this simple compound interest formula calculates is the amount of money you have earned simply by allowing your investment to sit for a certain amount of time. In this case, your investment earned you $2,165.10 in just 6 years.
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Using the Formula for Compound Interest to Make a Better Investment
Now that these calculations have been made, we can use the formula for compound interest to reveal the true benefits of compound interest. Let’s say that instead of gaining compound interest on our initial deposit of $7,000, we will put the money into a standard account that gains the same interest rate of 4.5% over the course of 6 years.
Since a standard account does not compound interest, every year your investment will add up to $315. This is calculated by multiplying 7,000 and 0.045 together. After 6 years of earning $315 in interest, you will earn a total of $1,890 in interest.
Without having to use the formula to calculate compound interest, you will see that your account will yield $8,890, instead of $9,165.10. In other words, by opening an account with compound interest, the compound formula shows that you will make $275.10 more after 6 years.
Now let’s play with the numbers a bit. If we change the t, or number of years to invest the money, from 6 to 10 in the compound interest formula, the results will alter dramatically.
Using the formula for calculating compound interest, we will get an equation that looks like this: A = 7,000 (1.00375) ^ (120). The only difference in this version of the compound interest rate formula is that the number of years has greatly changed the exponent. This means that we will multiply 7,000 by 1.56699, for a total of 10,969.
What the compound interest formula is telling us is that if we left our initial deposit in the account for an additional 4 years, we would gain nearly $4,000 in compounded interest.
Now let’s look at how much a standard account would make us in that time. Without using the compound interest formula, we can calculate that earning $315 per year for 10 years will result in $3,150 of interest, bringing our total account up to $10,150.
The results here are eye-opening. The difference in earnings between the two accounts is $819 (10,969 – 10,150). Based on the formula for compound interest, you will earn $819 more by investing your money using compound interest versus one that simply adds interest to your principal.
By using the formula to calculate compound interest, you will see how important it is to fully consider the amount of time you spend investing your money. When you invest for a shorter amount of time, like 6 years, you are only gaining $275 over a standard account, whereas in 10 years, the difference soars to more than $800.
Since the formula for compound interest clearly shows that the amount of time will be used as an exponent in the calculations, your earnings will literally grow exponentially. The longer you keep your money invested, the greater your overall earnings will be.
Therefore, the compound interest calculation formula will not only help you determine your future earnings, but will help you make an investment in the first place. Use this simple and compound interest formula to see just how long you should invest your money before you settle on the account.
A Closer Look at the Benefits and the Quarterly Compound Interest Formula
One question that gets asked a lot when using the compound interest rate formula is whether there is a quarterly compound interest formula to calculate earnings. The answer depends on how you look at the different pieces of the compound formula.
When we consider that n is the number of times interest is compounded throughout the year, there is no reason to have a separate quarterly compound interest formula. If your interest is compounded quarterly, then n, in the compound interest formula is 4.
By looking at it this way, the compound interest rate formula applies to quarterly, yearly, monthly, and all other types of compound interest schedules. Therefore, the formula for compound interest is capable of calculating any type compound interest account you are interested in opening.
Additionally, the compound interest formula will show you exactly how large of an initial payment you should make. When we look at the examples throughout this article, we have already seen how a larger investment time exponentially increases our earnings. With that being said, a higher P, or initial payment, will also have a great impact on how much money you collect.
Since the formula for compound interest is ultimately determined by multiplying P with the result of all other numbers in the calculation, the more money you invest, the more you will gain in the end. The same goes for the interest rate. As with all bank accounts, the higher the interest rate, the more interest you will gain.
Now say you want to buy a house in the future. By using the compound interest rate formula, you can determine exactly how much money to invest, how long you should invest it, and what interest rate you need to find in order to purchase your dream home.
The compound interest rate formula accounts for all of this information, and by simply adjusting one number or another, you can get the profit you are looking for. If you cannot increase your interest rate, you can simply let your money sit for longer, or t, to get the number you need.
The same goes for any investment. Maybe you do not want to buy a house, but you have your eyes on a car. Or a college fund. Or you’re looking for a way to retire. The formula to calculate compound interest will give you the numbers you need to make a smart investment.
Therefore, by using the compound formula, you will never step blindly into an investment. Your money will earn the amount you need without any of the risks that might be involved by simply investing a large amount.
Conclusion: Use the Compound Interest Formula to Your Advantage
While the compound interest formula may look intimidating, it is there for your benefit. As long as you have all the necessary information, you can punch each number into this simple and compound interest formula to determine exactly how big or how small of an investment you need to make.
If you do not feel comfortable using mathematical equations, practice the example we offered throughout this article. Write down a $7,000 investment over six years with an interest rate of 4.5%. Then, without looking, try to use the formula for compound interest to come up with the same answer we have here.
As long as you remember some of the basic rules, such as PEMDAS, the formula for calculating compound interest can become your best friend. As we have demonstrated, you can calculate your earnings to the cent.
It will also be important to look at the amount of money you would earn in a standard account. Maybe you haven’t been convinced that a compound interest account is right for you. By using the compound interest rate formula, you will see how big of a difference the two accounts will make.
Just remember that the compound formula is an ally. Use it wisely, use it often, and then watch your earnings add up.
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AdvisoryHQ (AHQ) Disclaimer:
Reasonable efforts have been made by AdvisoryHQ to present accurate information, however all info is presented without warranty. Review AdvisoryHQ’s Terms for details. Also review each firm’s site for the most updated data, rates and info.
Note: Firms and products, including the one(s) reviewed above, may be AdvisoryHQ's affiliates. Click to view AdvisoryHQ's advertiser disclosures.