Dennis Hammer is a writer and finance nerd with six years of investing experience. He writes about personal finance for Wealthsimple. Dennis also manages his own investment portfolio and has funded several businesses in the past. Dennis holds a Bachelor's degree from the University of Connecticut.
There’s an urban legend that Albert Einstein once called compound interest “the most powerful force in the universe.” We can’t be sure he really said it, but the sentiment is certainly true: Compound interest is a powerful finance tool for growing wealth.
But while Einstein had no trouble understanding compound interest, many people find it confusing. Even fewer know how to use the compound interest formula. In this article, we’re going to take a deep dive into compound interest. There’s a lot of math ahead of us, but we’ll walk you through it slowly.Wealthsimple offers an automated way to grow your money like the world's most sophisticated investors. Get started and we'll build you a personalized investment portfolio in a matter of minutes.
What is the compound interest formula?
Compound interest is the principle by which your interest earns interest. And then that interest earns interest. It goes on and on. As your balance gets larger, your interest payments grow larger, which in turn makes your balance larger. As you can imagine, compound interest adds up quickly.
If you’re familiar with simple interest, you’ll recognize some of the same variables in the compound interest formula, but with a few extra steps. Here’s the formula:
**Total principal and interest = P (1 + i)**n
Here’s what those letters stand for:
P = Principal of the loan (how much you’re borrowing).
i = Interest rate expressed as a percentage (e.g. for a 4% rate, use 0.04.)
n = The number of compounding periods. This will be different for each loan. Some compound yearly, some compound monthly, etc. You’ll find this information with your loan terms.
This equation will tell you how much you’ll pay back in total, including the original principal. It’s a great way to find out, for instance, exactly how much that car will cost you in the long run, or the real cost of your student loans.
If you want to find out just how much you’ll pay in interest, however, you simply subtract the original principal at the end of the equation.
Interest only = [P (1 + i)n] - P
This will tell you the cost of the loan. That is, you’ll learn exactly how much it costs for the privilege of borrowing money.
How to use the compound interest formula
Now that you know the formula, the next step is to learn how to use it.
Step 1: Solve the parentheses
Due to order of operations (remember that from math class?), we solve the parentheses of an equation first. There’s only one parentheses that needs solving in this case and thankfully it’s pretty easy. You just add one to the interest rate. If your interest rate is 2%, then the value in the parentheses would be 1.02.
Step 2: Solve the exponent
After solving the parentheses, you next solve the exponents. In the case of the compound interest formula, we raise the value in the parentheses to the number of compounding periods. If there are 12 compounding periods, we would raise our 1.02 to the 12th power to get 1.27.
Step 3: Solve for the interest
Our final step is to multiply what we’ve solved by the original principal of the account, investment, or loan. If you originally deposited $1,000, we would multiply that by 1.27 to get $1,270. This the total you would receive at the end of the loan term. Then you could subtract the principal to find out what you earned in interest: $1,270.
Example calculation of compound interest
Whenever we explore complex mathematical concepts, it helps to use a real life example to help us relate. Let’s walk through a fictional example of compound interest.
John has $15,000 he wants to grow. His bank is offering certificates of deposit at 3% compounded monthly, but his money will be locked in for four years. If he removes his money early, he’ll pay a big penalty. He wants to know how much money he’ll earn in interest.
Let’s go back to our formula. Total principal and interest = P (1 + i)n
If you remember from our formula, P is the principal, which is the $15,000 John wants to deposit in the CD. i is the interest rate, but since we don’t use 0.03. Banks state their yearly interest rates, but this CD compounds monthly, so we have to divide 0.03 by 12 months to get 0.0025. n is the number of compounding periods, which in this case is 36 (three years converted into month).
So here’s our equation: $15,000 (1 + 0.0025)36= $16,410.77
That’s how much John will get back at the end. That number includes his original investment plus his returns from interest. To find out just how much interest he earned, we simply deduct the original principal from that figure.
$16,410.77 - $15,000 = $1,410.77
To help you see how compound interest adds up over time, let’s look at all of the interest payments in one year of John’s certificate of deposit. This table shows you the starting balance at the beginning of the month, how much interest was earned that month, and the account’s ending balance.
|Month||Starting Balance||Interest Earned||Ending Balance|
Notice how the interest earned column increases over time. He earns more money per month the longer he holds the certificate of deposit. The difference isn’t enormous, but that’s because John only invested $15,000. Imagine if this were his retirement account with $200,000 or $300,000 earning 8-12% over 30 years across a diversified portfolio of exchange traded funds (ETFs). The interest adds up quickly.
Why does John care how much he will eventually earn in interest? Because we don’t invest in a vacuum. There are countless investment opportunities to grow your money. You need to understand how much interest you will earn from a particular security or investment product because so you can identify the investments that pay the most.
The benefits of compound interest
Hopefully you now understand how to use the compound interest formula. But that begs the question: Why is compound interest so important? What can it do for us?
1. Your money grows faster over time
Paying compound interest is troublesome because it can feel difficult to get ahead of the debt. Credit cards charge compound interest, which is why many people struggle getting out of credit card debt. Receiving compound interest, however, is wonderful because your money grows faster and faster over time. All you have to do is leave it alone.
When you put money into a high yield savings account, the interest you receive each period gets added to your balance. Your new balance is used to calculate the next interest payment, which includes interest you earned previously. Therefore, each interest payment you receive is slightly larger than the last (assuming you don’t withdraw any money from the account).
For example, reinvesting the interest returns of $10,000 could earn twice as much over 30 years than if you were to withdraw the gains.
This snowball effect is a powerful way to build wealth over time. It’s also why you should resist withdrawing money from your savings and investment accounts.
If you use an automated investment portfolio, it’s best to make regular contributions and pretend the money doesn’t exist until retirement. Every dollar you add to your balance creates a little more interest, and every bit of interest builds up your balance. This cycle is how people become wealthy.
2. Compound interest pays more than simple interest
The “interest of interest” effect means an investment with compound interest will always pay more than an investment with simple interest when all the other variables (principal, interest rate, and length of time) are the same.
Keep this mantra in mind: It’s best to pay simple interest and receive compound interest.
3. Compound interest is exciting and encouraging
It may seem silly, but watching interest grow in a savings account or an investment product is captivating—your money increases without having to contribute any of your labor.
In fact, the pleasure of watching money grow encourages people to leave their money in their investments and contribute more. It’s easier to commit money to investment if you can see significant, tangible growth each month, especially when you know that each dollar you contribute makes it grow faster.
4. Compound interest helps you reach your financial goals
The biggest benefit to compound interest is that it helps you reach your financial goals and prepare you for retirement. Stashing money under your mattress is technically saving for the future, but it doesn’t hold a candle to the power of a high yield savings account or investment portfolio. Without compound interest, you would have to work for every dollar of your nest egg.
Apply your new understanding of the compound interest formula any time you consider a financial product, investment, or loan. Make sure you understand the real cost or benefit of your money before making your decision.
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