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
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.
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:
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:
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.
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!