How Compound Interest Works & How To Calculate It

Key Takeaways


Compound interest is a double-edged sword. It can be your best friend or your worst enemy, depending on your situation. If you’re wondering, “how does compound interest work,” then you’ve come to the right place. It’s something that you should know about, whether you’re an everyday consumer or a seasoned investor. In this guide, we’ll explain what it is, how it works, and how to calculate it. Keep reading to better understand how this financial powerhouse can work either for or against you and how to get on the path to building wealth.

What Is Compound Interest?

Compounding is the process of growing something exponentially. With that in mind, you can think of compound interest as interest that builds upon itself. Simple interest is calculated using only the principal amount. In the case of compound interest, both the initial principal and the previously accumulated interest are taken into account. Thus, compounded interest grows much faster than simple interest. Some investors call compound interest the “money snowball effect” because it can lead to exponential growth for your money.

Compound interest formula

How Does Compound Interest Work?

It’s best to show you how compound interest works through a real example.

Let’s say you put $5,000 into a savings account. This savings account provides a 2% interest rate that compounds annually. At the end of year one, you’ll have $5,100. This is your principal of $5,000, plus $100 in interest earnings. It’s after the second year where you see compound interest starting to kick in. At the end of year two, your new savings total is at $5,202. This means that your interest earnings compounded from $100 to $202 in two years. By year 10, your initial principal of $5,000 will turn into a savings of $6,094.97. Thanks to compound interest, it will have grown over $1,000 without your having touched a thing!


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How To Calculate Compound Interest

Compound interest is your total principal plus its future value, minus its present value. It’s calculated by taking the initial principal and multiplying it by one plus the annual interest rate, raised to the number of compound periods minus one. This sounds complicated, but is much easier to understand by looking at the formula:

Compound Interest = P[(1+r)^n – 1]

In this formula, the “P” represents the total principal, the “r” represents the interest rate, and the “n” represents your number of compound periods.

Let’s take our example from above to show how this formula works. In this case, “P” is $5,000 (your principal), “r” is .02 (2% interest rate expressed as a decimal), and “n” is 10 (annual compound periods of 10.)

Compound Interest = P[(1+ r)^n – 1]


Compound Interest = $5,000 [(1+.02)^10 – 1]


Compound Interest = $5,000 [1.21899 – 1]


Compound Interest = $5,000 [0.21899]


Compound Interest = $1094.97

Using the formula, we were able to calculate that in 10 years, you will earn $1,094.97 in compound interest. Your total savings will be $6,094.97 (add the $1,094.97 interest to the $5,000 principal amount.)

If you’re interested in calculating the total savings amount including the compound interest, there’s another formula you can use:

A = P(1+ r/n)^nt

In this case, “A” represents the total savings, “P” still represents the principal, and “r” still represents the annual interest rate. What’s a little different in this formula from the previous one are the variables “n” and “t.” In this case, “t” represents your time horizon, and “n” represents the number of times the interest compounds each year.

Let’s apply this formula using the same example as above.

A = P(1+ r/n)^nt


A = $5000(1+ 0.2/1)^(1*10)


A = $5000(1.02^10)


A = $6,094.97

As we derived in the previous examples, the resulting amount of savings, including compounded interest, is $6,094.97.

In summary, these two formulas help you calculate either the compounded interest amount or the total savings, including the compounded interest. These formulas are pretty simple and easy to calculate, but it’s completely understandable if you have trouble committing both of these to memory. Instead, you can use a free online calculator, like this one offered by Moneychimp.com.

Compound Interest Growth

In our example above, the accumulated interest was just $100 after one year. After 10 years, however, the accumulated interest was a whopping $1,095. As a saver, compound interest is quite the wealth-building powerhouse. The best part is that you can put money into an account and forget about it. The compound interest will do its own work over time. Of course, you can build wealth even faster by adding to your principal amount at regular intervals. Bankrate.com provides an annual list of the best savings accounts with high yield interest rates.

Compound Interest & Debt

Compound interest can be your best friend when you’re growing your savings. However, it’s a double-edged sword. This is because compound interest can be your worst enemy if you’re borrowing instead of saving.

If you check out the interest rates on high-yield accounts, you’ll notice that they range between 0.6% and 0.8% at best. On the flip side, the interest rate on a personal loan can easily be upwards of 20%, depending on the principal loan amount and your credit score. (You can take a look at example loan rates on Bankrate.com.)

Here, you should notice that interest rates for loans are much higher than those for savings accounts. If compound interest helps savings accounts grow quickly, can you imagine how much more quickly debt will grow for borrowers?

This rate of growth can be damaging to your financial health. Living beyond your means is an easy way to get into debt quickly, especially when that debt grows exponentially. That’s why you should always strive to pay off your debts as soon as you can.

How to calculate compound interest

Taking Advantage Of Compound Interest

Now that we’ve gone over how compound interest can be used to your advantage or disadvantage, let’s focus on the fun stuff. There are some strategies you can implement so that when compound interest is on your side, you can maximize its benefits:

  • Save early! The benefit of compound interest increases over time, so it’s important to start saving early. As shown in the examples earlier on, you should have noticed that the total savings were much higher in year 10, as opposed to the first couple of years. If you can, make additional deposits as often as possible. You’ll be pleasantly surprised to see just how quickly your money will grow, thanks to compounding.

  • Compare interest rates: As a consumer, you should always shop around before committing to a product. Be sure to research different types of savings and investment accounts and their associated interest rates. How can you tell if the rate shown is an interest rate or a compound interest rate? Look for the term “APY,” which stands for annual percentage yield. You can start by comparing the rates of savings accounts and CDs provided by your bank, and then consider switching banks if you find one that offers a significantly higher rate.

  • Pay off your debts as soon as possible: If you have credit cards and loans, it’s in your best interest to pay them off as soon as possible. Paying just the minimum on these accounts will barely make a dent. You’ll find that you’ll accumulate interest faster than you can pay down your principal. One of the most common types of loans is student loans. Although it’s understandable if you can’t start repaying your student loans before you graduate, a smart move would be to pay down any accrued interest. This way, you can at least avoid interest charge capitalization and get a head start in paying down your balance. Also, if you focus on paying off your debts first and foremost, you’ll free up some cash flow that you can put toward your savings.

  • If you must borrow, keep the rate low: There will likely be times in your life where you’ll be forced to take out a loan. This could be for a car purchase, a home loan, or even an unforeseen emergency. Be a smart consumer by comparing products and interest rates. After all, the interest rate is what determines how quickly your debt will grow. If you have outstanding credit card debts, find out if there is a way you can consolidate your debt into one lower interest rate.

Summary

If you have more debts than savings, then compounding interest can feel scary. However, you have even more reason to ask yourself, “how does compound interest work?

Once you realize how significantly compound interest grows your debt, you’ll be incentivized to get rid of that debt as soon as possible. As you pay off debt, you’ll be freeing up more of your money so that you can start saving and building your wealth. If you need some help getting out of debt quickly, check out our guide on using the debt snowball method. As soon as you start enjoying the benefits of compound interest, you’ll be thanking yourself.

Do you have any other examples of how compound interest can be used to your advantage? Share in the comments below!

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