What Is Compound Interest?

When it comes to interest calculations, there are two fundamental options: simple and compound interest. Simple interest refers to a fixed percentage of the principal amount paid yearly. For instance, if an individual invests $1,000 at 5% simple interest for ten years, they will receive $50 in interest per year for a decade, no more or less. Bonds are an investment type that typically pays simple interest. On the other hand, compound interest is generated when investors reinvest their earnings, which accumulate interest as well. Essentially, compound interest refers to “interest on the interest,” and it is one of the reasons why investors are so successful.

Think of it this way: an individual invests $1,000 at a 5% interest rate. They receive a $50 interest payment after the first year. However, instead of pocketing the interest, they reinvest it at the same 5% rate. For the second year, the interest is calculated on a $1,050 investment, which comes to $52.50. If they reinvest that amount, their third-year interest will be calculated on a $1,102.50 balance, and so on. The principal (and the interest it generates) grow over time, thanks to compound interest.

Compound interest is calculated by applying an exponential growth factor to the interest rate or rate of return used. The formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate expressed as a decimal, n is the compounding frequency, and t is the time period in years. Principal refers to the starting balance on which interest is calculated, and rate refers to the interest rate expressed as a decimal. The compounding frequency indicates how frequently interest is added to the principal, while time represents the total time period in years. Common compounding frequencies include annual, semi-annual, quarterly, monthly, weekly, and daily, with the mathematical concept of continuous compounding involving constant accumulation of interest.

The Importance of Compounding Frequency in Calculating Compound Interest

When it comes to calculating compound interest, the compounding frequency can make a significant difference in the final amount earned. While annual compounding is commonly used as an example, interest can be compounded at other intervals, such as quarterly, monthly, or daily.

For instance, let’s consider an investment of $20,000 at 5% interest compounded quarterly for 20 years. In this case, the compounding frequency (n) would be four, reflecting quarterly compounding occurring four times per year.

It’s essential to distinguish between compound interest and compound earnings. Compound interest only accounts for interest payments generated by the principal amount, while compound earnings consider other investment returns such as dividends and appreciation in asset value. For example, if an investment in a stock generates a 4% dividend yield and a 5% increase in the stock’s value, the total earnings for the year are 9%, which is a form of compound earnings.

Although compound interest and compound earnings differ in their sources, both demonstrate the importance of long-term investing to maximize the effects of compounding. Compound interest is a powerful concept for investors because it enables even small amounts of money to grow significantly over time.