What Is Compound Interest? Definition, Formula, & More


Table of Contents:

  1. How does compound interest work?
  2. Example of compound interest over time
  3. How to calculate compound interest
  4. Understanding compound interest
  5. Compound interest considerations
  6. Compound interest FAQs
  7. The bottom line

Interest can be a beautiful or not so beautiful thing depending on its relationship with your finances. When you think about interest, you may think about it in two ways. The first is how it may contribute to your debt, and the second is how it’s possibly one of the best things that has happened to your savings or investments. Interest can make or break your finances. However, how you use it can work to your advantage.

So, what is compounding interest? Compound interest is when interest is earned on your initial principal balance and the accumulated interest from that principal amount. In its simplest definition, compound interest is interest accumulated on interest. Suppose you invested money in your savings account with a 5% annual interest rate. This means that next year you will earn 5% interest on the initial amount you invested, and in the second year, you will earn 5% interest on the initial amount you invested along with the accumulated interest on that investment. Compound interest can contribute to money growing at a faster rate than simple interest. Simple interest is when interest is earned only on the principal balance and not on the accrued interest.

However, when not managed properly, compound interest can work against you when it comes to borrowed funds. Compound interest can cause your finances to quickly spiral out of control if you have debt because of how much interest can accumulate over time. Contrarily, compound interest can also be one of the ways to build generational wealth when used properly. This is why financial literacy and understanding how to make your finances work for you and not against you is so important.

There are many components to compound interest. Whether you are saving for retirement, looking for effective ways to manage your money, or simply learning how you can benefit from your investments, understanding the benefits and risks to compounding interest can help you avoid financial pitfalls.

Key Takeaways:

  • What is the definition of compounding interest? The compound interest definition is interest accumulated on your initial deposit or loan along with its accrued interest or interest earned on interest.
  • Compounding schedules can range from a daily to an annual basis, but the time frame when the interest is actually credited or debited to/from the account can be different.
  • A compounding period is the amount of time between when interest compounds (at discrete intervals) or is credited to your account. The higher the compounding period, the more your money grows.

How does compound interest work?

As mentioned earlier, compound interest is interest earned on your initial deposit or accumulated on a loan along with its accrued interest. When you borrow or deposit money, the accumulation of interest on that money can depend on a few factors. Those factors include the interest rate percentage, the compounding period, and how much money is borrowed or deposited.

Let’s say you have a loan with compound interest of $2,000 with an annual interest rate of 12% that you plan to pay off in 5 years. You may initially think that this would be an easy feat to accomplish when taking into account the payoff time and loan amount. However, instead of just paying off the initial $2,000 you borrowed, a compound interest loan can add substantially more interest on your loan amount than a loan with a simple interest rate. In 5 years, your payoff amount would have risen to $3,524.68, adding an additional $1,524.68 to your $2,000 loan. However, if this were a $2,000 loan with a simple interest rate of 12%, the loan payoff in 5 years would equate to $3,200, adding $1,200 to your loan amount. The difference between the two is that the compound interest rate not only accrues interest on the principal balance or the initial loan amount of $2,000 but also on any interest that has already accrued on the $2,000. The simple interest rate, on the other hand, only earns interest on the initial loan amount of $2,000.

Now, let’s say, instead of borrowing money, you decide to invest $5,000 in a compound interest savings account with a 2% annual interest rate that has a yearly compounding period. This means that your initial $5,000 deposit and its accrued interest would be compounded annually. In 5 years, the interest earned on your principal balance would be $520.40, putting you at a total of $5,520.40. If the compounding period was monthly for a $5,000 deposit with the same compound interest rate of 2%, in 5 years, you would have earned $5,525.39.

Compounding schedules

The compounding schedule for savings and money market accounts is generally on a daily basis, while credit card accounts, mortgage loans, and personal business loans may have a monthly compounding schedule. However, other accounts, such as certificates of deposits, etc. may have a daily, monthly, or semi-annual schedule.

In addition to compound schedules varying, the time frame when the interest is actually credited to the account can be different. This means that the interest on an account may have a daily compounding schedule but may actually credit the interest on a monthly basis. You will only see the interest on your principal balance when it’s credited. In addition to the compounding schedule, the frequency of the compounding period has a large impact on how fast your money grows over time. Let’s delve a little further into compound periods.

Understanding compounding periods

A compounding period is the amount of time between when interest compounds or is credited to your account. In addition to the interest rate being a determining factor, the compound period is essential for the projection of your overall investment or loan. Compounding periods can take place annually, semi-annually, quarterly, and monthly. However, if the compounding periods are more frequent, this can contribute to your money or loan growing at a faster rate.

Example of compound interest over time

As mentioned above, a more frequent compounding period means the value of the sum will increase at a faster rate. Let’s assume you invest $5,000 that compounds annually at a 4% annual interest rate. We will explore the potential growth of this investment over a 5-year span.

$5,000 Compounded Annually at 4%

Year 1: $5,200

Year 2: $5,408

Year 3: $5,624.32

Year 4: $5,829.29

Year 5: $6,083.26

Now let’s compare a $5,000 investment that compounds monthly at a 4% annual interest rate over a 5-year span.

$5,000 Compounded Monthly at 4%

Year 1: $5,203.71

Year 2: $5,415.71

Year 3: $5,636.36

Year 4: $5,865.99

Year 5: $6,104.98

Conversely, if you were to apply this same example to a loan, in 5 years, a $5,000 loan compounding annually with a 4% annual interest rate would have grown to $6,083.26, or $6,104.98, if compounding monthly.

How to calculate compound interest

Using a compound interest calculator or other financial tools to calculate the compound interest formula may be easier than calculating it yourself. However, let’s take a look at how you can use the compound annual interest formula directly.

P(1+i/n)(n x t) = Amount (including compound interest)

P = principal or initial amount

i = interest

n = # of compounding periods

t = # of years

Let’s say you have a $1,000 loan over a 3-year time frame that has an annual interest rate of 12%, which is compounded monthly.

P= $1,000

i=0.01 (= 0.12/12)

n=12

t=3

1,000(1+0.12/12)12×3

Amount= $1,430.77

Understanding compound interest

How do you start using compound interest? When it comes to compound interest, you may be able to tailor specific strategies that work best for you and that meet your financial goals. However, there are a few things to keep in mind when starting your journey with compound interest. Let’s review.

  • Money growth over time

Compound interest can be an impactful tool to grow your money over time. Whether you are using compound interest with a savings account, money market account, certificate(s) of deposit, or investing in the stock market through dividend-paying stocks or mutual funds, there are many ways to use the principle of compounding. You may find that a specific way of compounding is worthwhile. The longer your money is held or saved, the stronger the potential of it growing over time.

  • Annual percentage yield (APY)

The annual percentage yield (APY) is the annual rate of return on an investment that includes the effect of compound interest. So, is it important to know your interest rate? In the case of investing, interest can be your friend. The higher the interest when it comes to your investment, the better chance it has of earning more money on your principal balance and accrued interest.

  • Compounding periods

As mentioned earlier, the compounding period frequency can impact the growth of your money over time. The higher the frequency, the more money and savings for the long term. Whether you are focused on how much you need for retirement or building wealth, researching or working with a financial advisor to make the best decisions for your investment is essential.

Compound interest considerations

There are a few other things to consider when using compound interest, including the time value of money (TVM) and the rule of 72. These are two tools that can work in close relation with compound interest.

Time value of money (TVM)

The time value of money (TVM) is the concept that the total amount of money that you have on hand or in real time is worth more now than the same amount would in the future because of its potential to earn more by growing over time. Let’s say you have the option to receive $100 today or 2 years from now. You may choose to receive the $100 today because it has the potential to grow over time, making it worth more than receiving the $100 2 years from now. In 2 years, the $100 could decrease in value and purchasing power due to inflation and other factors. The $100 in 2 years equates to keeping the $100 in your pocket for 2 years. In your pocket, it doesn’t earn interest, but if invested, it has the opportunity to earn interest and increase over time.

There may be different variations when using the TVM formula. The future value formula shows how much your money will be worth in the future, while the present value formula shows how much money you will need today to earn the future value over a certain period of time. Investors can use the TVM formula to see the potential of their investment growth with compound interest.

PV x (1 + i)n= FV

FV / (1 + i)n= PV

pv= present value of money

i= interest rate

n=# of compounding periods in a year

t= number of years

fv= future value of money

Rule of 72

When starting your investing journey and thinking about how stocks work and how to invest in them, a question that may come to mind may be how does compound interest work with stocks? While interest rates don’t apply to the stock market, the principle of compounding does. Investors may apply compounding by choosing to hold stock for a long period of time and reinvesting the gains they make from the investment into the same stock. In addition, the principle of compounding can also be applied to an investor’s overall portfolio. Investors may look at their entire investment portfolio as an asset and focus more on the appreciation and longevity of their overall portfolio rather than a single stock by reinvesting any gains back into the portfolio. The principle of compounding can be effective depending on your strategy and financial goal as an investor.

Moreover, the idea when investing in the stock market is that the value of the stock that you invest in will increase. This means that if you were to purchase 5 shares in ABC company, and over time the value of ABC company increases, your investment in the company would as well. This is called a return on investment, which is different from the return on investment you would get from compound interest on a savings account. Unlike the guarantee of a compound interest rate staying the same on a deposit or loan, you can’t rely on a guarantee that the value of stock will continue on an upward trend in the stock market due to its volatility or that your return on investment will remain the same over time. Because of this, investors may look to the rule of 72 to help them gain insight into the future performance of their investment portfolio.

The rule of 72 is a formula that allows investors to see how many years it will take for their money to double at an annual rate of return. When investors use the rule of 72 for the stock market, they are essentially predicting how many years it will take their investment to double based on the average rate of return of how the investments have performed in the past. Let’s say, on average, your investment has performed at a rate of 6%. Therefore, you predict that it will continue to perform at that rate, and you want to plan for a 6% return in the future. Let’s plug that into the 72 rule formula to see how long it will take for your investment to double.

72/R = T

R= interest rate or expected growth rate

T= # of years it takes your investment to double

72/6 = 12 years

In this case, it will take 12 years for your investment to double as long as the market continues as expected. The rule of 72 can be used for anything that grows at a compounded rate of return annually, such as loans, gross domestic product, inflation, etc.

In the case of compound interest with a savings account, you may want to see how long it will take for your deposit to double. Suppose you invested $1,000 in your savings account with a compound interest rate of 8%. By using the 72 rule (72/8), you will find that it will take 9 years for your investment to reach $2,000 at an 8% annual interest rate. Using the same scenario, let’s say you have credit card debt or have borrowed money. In 9 years, the amount owed on your credit card or loan will double.

Compound interest FAQs

  • How does compound interest compare to CAGR?

Compound interest is interest earned on the principal balance along with its accumulated interest. However, compound annual growth rate (CAGR) is the annual return on an investment that’s determined by calculating the initial balance and any interest accrued over the years.

  • Can compound interest make you rich?

There are many effective strategies for compounding. However, depending on the strategy, compound interest can help you build wealth over time depending on your financial circumstances.

  • How do we calculate compound interest?

As mentioned earlier, compound interest can be determined by using the following formula.

P(1+r/n)nt = Amount (including compound interest)

The bottom line

Compound interest can be a powerful tool that can add to your financial health or take away from it. It has the potential to completely break the bank or substantially add to it. It’s important to understand the effect it can have on your finances over time. If you have debt or a loan, the fewer compounding periods and the lowest interest rate can benefit you the most, while the most compounding periods and the highest interest rate can benefit your investment the most. Whatever side of finances you land on, it’s important to understand the benefits and risks when using compound interest. Sign up now for the Public App to learn more about investing.

The above content provided and paid for by Public and is for general informational purposes only. It is not intended to constitute investment advice or any other kind of professional advice and should not be relied upon as such. Before taking action based on any such information, we encourage you to consult with the appropriate professionals. We do not endorse any third parties referenced within the article. Market and economic views are subject to change without notice and may be untimely when presented here. Do not infer or assume that any securities, sectors or markets described in this article were or will be profitable. Past performance is no guarantee of future results. There is a possibility of loss. Historical or hypothetical performance results are presented for illustrative purposes only.

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