What is compound interest and how does it work?

Have you ever wondered how to make your money work harder? You may have heard people talk about harnessing the power of compound interest but have not been quite sure what it means or how it works. Taking advantage of compound interest in a savings account can help smart savers save even more. But if you’re new to saving, you might not be quite sure what compound interest is.

How does compound interest work? At its most basic, compound interest is the interest you earn on your original deposit plus the accrued interest. That’s a bit of a brain tickler, we know. So, Spruce is here with a full explanation that will help you understand — and make the most of — compound interest.

Did you know with Spruce you can opt in to earn interest and take advantage of compounding interest today? With Spruce, you can benefit from daily compounding interest and earn 3.50% APY^{Disclaimer number12. Go to disclaimer for more details.} on every penny on your Savings Account. In fact, Spruce offers you up to two interest-bearing saving goals and an Extra Saving account — all with no sign-up fees, minimum balance requirements or monthly fees!

Check out our Help Center to find out how to opt in to start earning interest today. Learn more about Spruce savings interest.

Spruce fintech platform is built by H&R Block, which is not a bank. Bank products by Pathward®, N.A., Member FDIC.

Now, let’s dive into the details of compound interest.

How does compound interest work?

To get started, it can help to understand simple interest vs compound interest.

What makes simple interest so simple is that it’s only calculated based on the initial deposit, known as the “principal” amount.

So, if you put $1,000 in a savings account with a 5.00% simple interest rate,*

• Year one: You start with $1,000 and earn $50 in interest.
• Year two: You start with $1,000 and earn $50 in interest.
• Year three: You start with $1,000 and earn $50 in interest and so on ….

*Assumptions: The account will not compound annually. The principal remains untouched (no withdrawals/deposits) during the hypothetical timeframe.

As you can see, with simple interest, the principal amount would never reflect the accumulated interest from prior years, so you would continue to earn $50 every year after.

But when compound interest enters the scene, it kicks things up a notch as the interest you earn, earns interest by taking into account the principal amount and the interest accumulated over time. 

Let’s say you start with that same $1,000 principal amount with a 5.00% interest rate that compounds.*

• Year one: You start with $1,000 and earn $50 in interest.
• Year two: You start with $1,050 (adding in the $50 you earned in year one) and earn $52.50 in interest.
• Year three: You start with $1,102.50 …. and so on

*Assumptions: The account will compound annually. The principal remains untouched (no withdrawals/deposits) during the hypothetical timeframe.

Although the additional $2.50 you earned on the compounded interest from the example might not sound like a lot at first, compound interest helps your money grow exponentially. Imagine a snowball effect where over time — say, several years — your money grows more and more. As a result, taking advantage of compounding interest can boost your savings over time. Not too shabby!

Compound interest frequency — Take note!

Where APY is concerned, timeframes matter. That’s why you always want to pay attention to the details. Specifically, compounding interest periods are the time intervals between when interest is added into your savings account. The frequency could be a number of timeframes:  compounding daily, compounding monthly, compounding annually, etc. 

With this in mind, the compounding interest example above would change based on when the compounding occurs. If interest is compounded more frequently than annually, such as quarterly, monthly, or even daily, the total amount at the end of two years would be slightly higher due to more frequent compounding.

How to calculate compound interest with examples

With these basics under your belt, let’s take a closer look at the math. Don’t worry, we’ll make it as painless as possible.

Compound interest formula

First, let’s talk about annual percentage yield, or APY. This is the total amount of interest you earn on money in your savings account in one year. APY includes the interest earned on the original balance in your account, assuming it doesn’t change, plus any compounded interest previously earned.

To calculate APY, you have to consider two main factors:

1. the interest rate and
2. the number of compounding periods (annually = 1, quarterly = 4, and monthly = 12, etc.).
   
   Then, you can multiply the APY by your original deposit amount to see how much you’d earn from it. If math is your jam, here are the variables and the actual formula:

(1 + r / n)ⁿ -1 = APY  

In this formula,

r = interest rate (expressed as a decimal)
n = number of compounding periods

Below we outline an example, using a hypothetical APY of 2.00% to illustrate.*

If you deposit $500 for one year with an 1.98% interest rate (with monthly compounding), you’d have an APY of 2.00%.

 (1 + 0.0198 / 12)¹² – 1 = 0.019881 or 2.00%

To calculate how much your principal amount will earn in interest over 12 months (with monthly compounding), you can multiply the APY by your account balance of $500.

500 X 0.0200 = $10.00

At the end of one year, your new principal will be $510.00. Learn more by reading our post about APY vs. interest rate.

*Assumptions: The account will compound monthly. The principal remains untouched (no withdrawals/deposits) during the hypothetical timeframe.

See what daily compounding could look like for a Spruce Savings account at 3.50% APY^{Disclaimer number12. Go to disclaimer for more details.} with our savings interest estimating tool.

Compound interest savings account

As you can see, compound interest enables the money in your savings account to grow faster over time. As your principal and interest earnings grow, your potential for growth increases as well. Compound interest is a way to make your money work harder for you, as your balance increases without you lifting a finger.

A compound interest savings account allows you to add to your savings quickly, whether you’re saving for a car, a house, or your child’s education. It can also help you build an emergency fund for unexpected expenses. The accumulated savings can help provide a safety net and reduce financial stress.

And when it comes to long-term goals, compound interest is a critical component of reaching them. Saving consistently over the years and benefiting from compounded interest growth can help you build a nest egg. Need help finding ways to save? Check out this article for even more money saving tips.

How Spruce can help you save on top of earning interest with your savings

Spruce offers many features that can take the guesswork out of saving. With Spruce, once you opt in*, you can benefit from earning interest on your savings in your Extra Saving account and in two saving goals that you can easily set up. Plus, you can name your saving goals according to your plan for the money, such as “new laptop” or “vacation.” Then, you can set up an automatic transfer to fund your goals or make transfers manually, according to your own schedule.

What’s more, features like automatic round up and cash back rewards^{Disclaimer number1. Go to disclaimer for more details.} make saving simple.

• Round up: When you use your debit card, we’ll round up the transaction to the nearest dollar and deposit the difference in your Extra Saving account.
• Cash back rewards: Earn money when you shop from select retailers you know and love. The money you earn goes straight into your “Extra Saving” account.

Saving is easy when you keep a close watch on where your money is going, and you can spot overspending. Spruce makes this easy with a handy budget tracker tool. The mobile app automatically categorizes your transactions to keep you aware of how much you’re spending and where you might need to cut back. Use the Watchlist to pick areas that you’d like to keep an especially close eye on to make sure you’re on track each month.

Unlike some banks, Spruce doesn’t have account balance minimums or charge for creating separate places to save your money. And there are no sign-up fees and no monthly fees to worry about.

And last but not least, Spruce deposits are FDIC insured by the Federal Reserve Bank — up to $250,000, the maximum allowed by law — so you can rest easy knowing that your accounts are safe.

Check out our Help Center to find out how to opt in to interest with Spruce.

Take advantage of compounding interest with Spruce today

Spruce has the tools to help you take control of your finances. Ready to take advantage of earning 3.50%% APY^{Disclaimer number12. Go to disclaimer for more details.} on your savings balances and all the other features Spruce has to offer? 

Get started with Spruce today! And then follow the steps to opt into interest with Spruce.  

This information provided for general educational purposes only. It is not intended as specific financial planning advice as everyone’s financial situation is different.