Compound interest is a concept in finance that allows your money to grow exponentially over time. It is the interest calculated on both the initial amount of money you have (known as the principal) and the accumulated interest from previous periods.

Here’s how it works:

Let’s say you have $1,000 that you invest in a savings account that pays an annual interest rate of 5%. At the end of the first year, you would earn $50 in interest (5% of $1,000). So, your total balance after one year would be $1,050.

Now, compound interest comes into play. In the second year, instead of calculating the interest based on the initial $1,000, the interest is calculated based on the new balance of $1,050. Assuming the interest rate remains at 5%, you would earn $52.50 in interest (5% of $1,050). Therefore, your total balance at the end of the second year would be $1,102.50.

As you can see, the interest earned in each subsequent year is based on the new total balance, including the previously earned interest. This compounding effect is what makes compound interest powerful over time.

The formula to calculate compound interest is:

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

Where:

A = the future value of the investment/loan, including interest

P = the principal amount (initial investment/loan)

r = the annual interest rate (expressed as a decimal)

n = the number of times that interest is compounded per year

t = the number of years

It’s important to note that compound interest can work for you when you are earning interest on investments or saving accounts, but it can also work against you when you have loans or credit card debts that accumulate compound interest over time.

In summary, compound interest allows your money to grow exponentially by reinvesting the interest earned, leading to greater returns over time.