Compound Interest | Does it Work?

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Compound Interest, does it work? A question many people ask themselves when thinking about saving or investing. The short answer is ‘yes’. However, most people only think about compound interest when it comes to investing or saving because that’s people like to bring it up, but they fail to acknowledge how it can also work against you.

Alber Einstein once said, “Compound interest is the 8th wonder of the world. He who understands it… earns it. He who doesn’t… pays it.”⁠ Many fail to grasp the importance of this concept, and how applicable it is to our every-day lives.

In this quote, Einstein suggests that compound interest can work with you —an investment growing over time— or against you —paying down debt over time.  

Understanding how compound interest impacts our every-day lives gives us the opportunity to find ways to use it to our advantage and ways to avoid its hostility.

What is Compound Interest? How Does it Work?

Compound interest is the accumulation of interest over time. It is referred to as ‘compound interest’ because interest is earned on top of interest. Over time, this leads to exponential growth.

When interest is earned on a principal, that interest now becomes part of the principal. The next round of interest will be earned on the new (larger) principal. This is referred to as “compounding.”

Whether this interest is accumulating on a savings account, an investment, or a debt, the interest is compounding, sometimes at different rates (daily, monthly, annually).

How Compound Interest Can Work In Your Favor

Savings Account

Let’s say you put $10,000 into a savings account paying a 5% interest rate. This interest rate is referred to as an annual percentage yield (APY) which is interest earned on your account, compounded annually.

At the end of your first year, you will have $500 of interest paid to that account, making your total principal $10,500. Keep in mind that this interest is compounded annually, so even though you might get an interest payment each month, you will only be getting one-twelfth of the total each month. Hence the annual percentage yield. 

Moving on to the end of your second year, you will have a new principal of $11,025. That’s a $10,500 principal at the start of your second year from your first year of interest, plus $525 of interest earned throughout your second year.

Fast forward by 10 years, and that principal has grown to $16,289. This may not seem like big growth but if we fast forward to the 40-year mark, that initial principal has now grown to $70,400. And all you did was put $10,000 into an account one time

Investment Account

The greatest benefit of compound interest when it comes to investing is that the earlier you start the less you need to start with because time is on your side. The example above is a great demonstration but not everyone has $10,000 to start right off the bat, we simply used a round number for the sake of simplicity.

Let’s look at a more realistic example. Let’s say you invest in an S&P Index fund. Historically, the S&P has given a 10% annual return. If we account for an average 2% annual inflation rate, it reduces it to 8% (10% – 2% = 8%). 

Now, let’s say you invest $160 per month into this fund. If you continue this small investment for 40 years, it’ll grow to $522,165 (excluding dividend reinvestments). All that you’ve contributed over the 40-year course was $76,800. This example is illustrated in the image below.

When applied to investments, the biggest benefit of compound interest is that the earlier you start on a consistent investment, the less you need to contribute to it. Even if you discontinued the contributions, your investment would continue to grow thanks to compound interest.

How Compound Interest Can Work Against You

As mentioned earlier, compound interest can work against you just as well as it can work with you. Hence Einstein’s quote, “he who doesn’t understand it, pays it”. 

Compound interest works against you when you apply it to a loan or other type of debt accruing interest over time. In this case, the interest being accrued is referred to as the annual percentage rate (APR) as opposed to APY. APR is based on the interest rate, but it also takes other variables into account such as points, additional fees, and other associated loan costs. In short, it is the cost of borrowing money. 

A sneaky little thing about loans though is that APR does not account for the frequency at which your interest compounds. So always make sure to read the fine print on a loan or credit card to get the most accurate idea of what you’ll pay in interest.

Now, let’s look at a common example adopted by about 70% of Americans today, credit cards. Credit cards compound at different rates, however, many of them compound on a daily basis. In this case, they will actually multiply each day’s average balance by the account’s periodic rate, and then add that amount to the next day’s average daily balance.

This means that interest is added to your debt (the principal balance) every single day. This accumulation of interest will begin whenever you miss a payment on your card. If you don’t pay off the new balance, the interest rate then applies to the new (larger) balance the next day. In other words, the interest compounds on a daily basis.

This is why it’s important to be responsible with your credit cards and pay them off on time every single month. This way, you won’t accrue any interest on your debt at any point in time. And when it comes to larger loans (such as a mortgage), always make sure to understand how the interest accumulates and how frequently it compounds.

Knowing these small details will help you avoid loans that may be out of your paygrade. Remember, the more frequently your interest compounds, the more it will accrue over time. The higher the APR, the more interest will be added per compounding period. 

Calculating APR is not as simple as calculating APY because every loan and credit card have different conditions in terms of account points, additional fees, and other associated loan costs. To figure out how much you will pay for a specific loan or credit card, always ask exactly what’s included and how frequently it compounds.

The variables included in loans can make the calculations more complicated, but the overall lesson here is this: the higher the APR on your loan account, the more interest you pay on a given balance. Always know the small details that are not included in the advertised APRs.

How to Calculate Compound Interest

If you’re someone who likes to see things happen on paper, the formula to calculate how much interest is accruing on your account is as follows:

calculation of compound interest

 

Fortunately, in today’s easy tech era, you don’t need to be a math wizard to make this calculation. There are a number of online calculators that can do this for you. All you need to do is plug in the values into their designated sections. 

This formula does not apply to APY or APR  but compound interest alone. If you want to calculate APY, the formula is as follows:

calculation of apy

This formula does not account for APR because APR takes other variables into account.

Compound Interest in Relation to APY & APR

As said repeatedly throughout this article, compound interest is the interest added, at a given frequency, to the principal, affecting the total amount earned or owed. 

When it comes to APY, the interest rate and the frequency at which it compounds is included in the APY. However, when it comes to APR, it refers to what you owe and does not reflect the frequency at which it compounds. 

apy vs apr

These hidden fees and the frequency of compounding can work against you, and can quickly add up! Always be sure to read the fine prints and know the applicable fees to get the most accurate view of what you could end up owing.

By understanding how compounding works, you can make more strategic financial decisions. For example, if you’re shopping around for a lucrative savings account, you should probably be looking for an account with a higher APY or one that compounds more frequently. And when looking for a loan, always know the associated costs, the frequency of compounding interest, and how high the rate is.

If you have any feedback, I highly encourage you to leave it in the comment section below. Thank you for reading, and have a lucrative day!


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24 Comments

  1. Thank you for the information concerning compound interest. when it comes to money, I’m not very responsible, so it’s nice to know a little bit more. Not knowing how to use the system is difficult when you don’t know the inner workings of it. I never knew exactly how interest worked and never considered committing to saving money.

    1. Glad to see you on here then, welcome aboard!

  2. I never understood how compound interest worked I saw it explained here.   Thank you for a clear overview of this concept and how it can help and hurt you.  It never even occurred to me that my credit cards were costing me so much money!!!  You’ve inspired me to work harder to pay them off.

    1. I’m happy to help 🙂 glad this was helpful

  3. This is a great article explaining with details the advantage and disadvantages of compound interest. a lot of folks out there do not pay attention to their credit debt as it gets compounded over time and adds up more that to their credit. So this is an educational and beneficial post that can help folks get a better understanding of the negative part of compound interest and saving them a lot of money that can stay in their pocket instead of going to creditors for no good reason.

    1. Absolutely true!

  4. Wow, I loved that Albert Einstein quote. That’s so well said. I’ll have to write it down. But regardless of that, I believe the article was superb.

    I really loved your style of writing. Not only was it very easy to follow and well-structured, but also I loved the examples that made the matters and ideas you were trying to put across far more grasp-able (if that’s a word). And thank you for taking your time to create those two sort-of infographics. Personally, I’m a huge nerd on formulas like that. To me, it makes the whole thing a lot more feasible and paints the picture even more clearly. I hope that makes sense. 

    Oh, and, yes, that one in the end when comparing the earn and pay, loved it. Well done!!

    1. Thank you! Glad to hear that this was easily understandable haha I know compound interest can get a little complicated so I try to simplify it as much as I can

  5. Wow

    I am so glad I came across this article today. I am actually one of those people who did not know that compound interest can work against you and that sadly if you don’t understand it, you pay it. 

    I have learnt so much today and am even going to destroy my credit card. I shall not be using it anymore as paying them on time every single month for me has failed month after month.

    From now on I will be working making the compound interest work for me using the great examples you have outline in your article.

    By the way, I have also bookmarked your website for future reference and to learn more on finances.

    Regards

    Boi

    1. Glad to hear that! 😀 It takes a lot to come to the realization that credit cards can sometimes be doing us more good than bad! I always believe that if credit continues to be stacking on them, it’s probably best to just get rid of them. Thank you so much for your feedback 🙂

  6. Misael! first, your setup is fantastic. The domain name, the layout and your writing are all great. I love the “Spread the Wealth” tag, too. Second, thank you for doing this article. I recently finished college, and am way too familiar with credit cards and loans lol. I had never fully been able to wrap my head around the processes behind my accumulating debt, and spent a lot of time scratching my head and wondering why I owed what I owed. Thank you for clarifying all of this!

    1. Derek, thank you so much 🙏🏽 for the feedback on the page. I’m glad it’s a good layout. And yes, unfortunately, debt stacks up VERY fast and it’s very sneaky. I’m very happy to hear that this article has been helpful 😊

  7. What a fascinating article, I had to read it as I like to understand money. I’ve known for years about compound interest on savings but I had never thought about compound interest on debts. I’m so pleased that you bought this to my attention as I’ve had mortgage loans in the past and fortunately it didn’t catch me out and I have now completely paid it off.

    I will be very wary in the future. I’ve always paid all my credit card payments every month and in 40 years have never paid interest just a low yearly fee. It always pays to be money wise. I loved the calculations.

    1. That is excellent! Congratulations on getting those mortgage loans paid off! You really saved yourself a lot of money. And the fact that you always pay your credit cards on time is also amazing! In case you would like to know, however, there are credit cards available that do not charge a yearly fee. A great example is the Discover credit card option. They don’t charge a yearly fee, they offer Great cashback matching benefits, and you can use this link to get a $50 bonus for signing up!

      Btw, if you do end up signing up. Let me know what you think. I’ve personally had a great experience with this card, I’m sure others will too.

  8. Hi Misael! Wow, that’s a fantastic explanation on how compounding interest works. I’ve always found financial and accounting matters to be complicated and twisty, although I enjoyed your simple infographics and differentiating the key highlights of APY and APR, as previously I did not have a clear understanding between these two! 

    Couldn’t agree more on aspect of credit card usage and to pay them timely; especially nowadays people tend to overlook the hidden piling interests when missing card payment. Even registering for a card can be quite tricky in knowing how the interest develops and so forth.

    Thank you for simplifying the points of compounding interest, I would share this with my friends and family who are looking in improving their financial responsibility and awareness! Great article and solid information!

    1. Yeah playing for any loan can be very tricky unfortunately. But that’s where we have to be educated on what we’re getting into. Thank you for your feedback

  9. Hi there, You could not have said it better. Thank you. Most people are never taught finances so they have to learn the hard way. I love how you broke down Albert Einstein’s quote. It has so much more meaning by doing this. I hope a lot of people read this article and take it to heart. Once someone realizes how much they are spending on the compound interest they will stop using credit cards.

    1. Although my goal is not to stop people from using credit cards, I do admit that the majority of people are better off without them. For those who allow their credit cards to accumulate interest, they should be trying to avoid them and get into a better behavior with them. But if you can use credit cards wisely, compound interest may not affect you in a negative way. I think we can use it to our advantage

  10. Thank you Misael, for this explicit information on compound interest. I knew about the hurtful part of it but I did not know how bad it could hurt. It is so shocking to realise the daily growth of debt on a credit card. It is good to pay off credit cards and stop relying on them. I would rather be on the helpful side of compound interest. 

    1. 100% agree!

  11. Thank you for providing such a detailed info about this not so interesting topic, but people understand they need to think about it usually when it is too late already. Honestly i have no idea how compound interest actually work, but from your article is more less easy to understand it even for someone like me. Thank you for this info.

    1. Of course 🙂

  12. Hello, I’m falling in love with your blog. I really liked this article too. I couldn’t help but read your about page too. I also think the idea of your blog and also the name of it is really good. I really love your blog and to be sincere, I would like to connect on Facebook if you don’t mind. 

    Managing finances is one of my hobbies too, but I’m not as technical as you. Did you study finance or something similar at University too? 

    I really like your guides and I will be following your blog as your guides are very detailed and newbie friendly. 

    1. I wouldn’t mind at all! Send me an email to support@thenerdfinance.com to connect! I’m glad you like the information 🙂

      I’ve done my fair share of university studies in finance, I’m currently still in school for my finance major, but I’ve learned a lot more about it from actual experience and my own research, rather than school. 

      Thank you so much for your feedback and for sticking around 🙂

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