What Is Compound Interest, And How Exactly Does It Work?

A graph showing the linear growth of simple interest and the exponential growth of compound interest (via experian.com).

In finance, few concepts are as fundamental to understanding both the basics and real-world applications. One of these concepts is compound interest, which is often described as “interest-on-interest.” Compound interest has the ability to turn small savings into a significant amount of wealth over time. On the contrary, it can also drain existing savings when one borrows money through loans and doesn’t pay careful attention. This is why it can play a central role in banking, investing, and debt, making it a concept that everyone should know about, regardless of their profession, status, or age.

What Is Compound Interest?

Compound interest is the process by which interest accrued on an amount of money is added back to the principal, with subsequent interest payments being calculated based on the new principal. Theoretically, it’s a never-ending process that allows for the total to grow exponentially over time. In other words, interest on the initial deposit or loan is added back to that balance, and future interest payments are recalculated based on the new balance. This means that if left untouched, the interest payments will become larger and larger every pay period. This can be good or bad, depending on whether it involves compound interest on a loan, in which you have to pay the bank, or a savings account, in which the bank has to pay you. 

To make the concept of compound interest easier to understand, we will look into an example. If you deposit $1,000 into a savings account with a 5% annual interest rate, you would earn $50 in interest after the first year, leaving you with a total of $1,050. In the second year, however, you would earn interest on the $1,050, rather than simply on the original $1,000. After the second year, you would have $1,103, earning approximately an additional $53. Then, the third year, you would start off earning interest on the new balance of $1,103. Over many years, this effect will accelerate, creating a snowball of growth. The longer the money stays in the bank account, the more rapidly your deposit will grow.

Factors That Determine Growth With Compound Interest

Before we get into the four key factors that determine by how much or how quickly your savings or loan will grow with compound interest, it is important to know about the formula used to calculate the effects of compound interest. The formula can be found below, where “A” is the balance (final amount), “P” is the principal (initial amount), “r” is the interest rate (expressed as a decimal), “n” is the number of compounding periods in a year (eg. quarterly compounding would mean n = 4), and “t” is time (expressed in years):

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

With that in mind, we can now discuss the four determining factors observed in the equation above: 

• Time: As we talked about earlier, the longer your money remains invested or saved, the longer it has to grow. Even small amounts can become substantial if left untouched for many years and put in a compounding account. On the other hand, compound interest can also come back to bite you if loans are taken out and left unpaid for too long.

• Frequency of Compounding: Interest can compound annually, quarterly, monthly, or even daily. The more often it compounds, the faster your balance increases. This can be seen in action if you apply the mathematical formula for compound interest and manipulate “n.” Feel free to test the formula out with some numbers!

• Principal: The larger the principal is, the higher the amount by which it grows will be. The principal does not affect the rate of growth; rather, it only affects the actual amount of growth.  

• Interest Rate: Of course, last but certainly not the least, we have the interest rate itself. This does not need much explanation, as a higher interest rate will lead to faster growth of savings or loans, while a lower interest rate will lead to slower growth.

These four factors are the reason why financial experts emphasize starting to save or invest early because when combined, they can transform even modest contributions into large sums. These factors are also the reason why experts advise people not to ignore loans or take them lightly, as they can quickly turn into an insurmountable problem.

Compound Interest in Savings, Investments, and Debt

For savers and investors, compound interest is a powerful ally. Retirement accounts, certificates of deposit, and many other financial tools rely on compounding to grow wealth. By investing earnings rather than withdrawing them, your money will continue to work for you and generate more income over time.

While compound interest can work in your favor significantly, it can also work against you when it comes to borrowing. Credit cards are a key example of this, as they often use compound interest to calculate outstanding balances and payments. If a borrower does not pay off their balance in full, interest and interest-on-interest will be added to the amount owed. Soon enough, the interest itself will start to accumulate, eventually leading to the amount of interest owed being more than the initial debt itself.

For example, if you borrow $10,000 through a credit card at an annual interest rate of 25%, you would owe over $93,000 after just ten years. When using simple interest instead of compound interest, you would owe a much smaller $35,000 after ten years. This is exactly why paying off high-interest debt quickly is critical. The same force that grows savings can also make debt spiral out of control if ignored.

Conclusion

Compound interest is one of the most important topics to learn in personal finance because it can create extraordinary results from ordinary amounts of money. By starting at an early age, saving regularly, having a balanced budget, and staying consistent, you can utilize the power of compounding to build lasting financial security, which can especially help you during retirement. However, compound interest can also be dangerous in the context of unmanaged debt. Understanding compound interest and utilizing it properly is the key to making money work for you rather than against you.