What is compound interest?

Compound interest is the process by which interest earned on an initial amount of money (the principal) is reinvested so that, in future periods, interest is earned not only on the original principal but also on the accumulated interest from previous periods. This effect causes the investment or loan balance to grow at an increasing rate over time. In finance, compound interest works by calculating interest periodically—such as annually, semi-annually, quarterly, or monthly—and adding it to the principal. For example, if you invest $1,000 at an annual compound interest rate of 5%, after the first year you earn $50 in interest, making your total $1,050. In the second year, you earn 5% not just on $1,000 but on $1,050, so your interest for that year is $52.50, and your total grows to $1,102.50. This compounding effect continues to accelerate the growth of your investment or debt over time. Compound interest is a powerful concept in finance because it rewards long-term saving and investing. The more frequently interest is compounded and the longer the time period, the greater the growth. Conversely, compound interest can also increase the cost of borrowing if interest accumulates on unpaid loan balances. Understanding how compound interest works helps individuals make informed decisions about saving, investing, and borrowing.

Compound interest is the process by which interest earned on an initial amount of money (the principal) is reinvested so that, in future periods, interest is earned on both the principal and the accumulated interest from previous periods. In other words, it’s “interest on interest,” which allows your investment or loan balance to grow at an accelerating rate over time. In finance, compound interest works by calculating interest not just on the original principal but also on the interest that has been added to the balance in prior periods. For example, if you invest $1,000 at an annual compound interest rate of 5%, after the first year you earn $50 in interest, making the total $1,050. The next year, the 5% interest is applied to $1,050, so you earn $52.50, and this process continues, causing the amount to grow faster than with simple interest, which is only calculated on the principal. Compound interest can be compounded at different intervals such as annually, semi-annually, quarterly, monthly, or daily, and the frequency of compounding affects how quickly the investment grows. The formula to calculate the future value with compound interest is: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] where: - \(A\) = the amount of money accumulated after \(t\) years, including interest - \(P\) = the principal amount (initial investment) - \(r\) = annual interest rate (decimal) - \(n\) = number of times interest is compounded per year - \(t\) = number of years Understanding compound interest is crucial for making informed decisions about savings, investments, and loans, as it significantly impacts the growth or cost of money over time.

Compound interest is a fundamental concept in finance where the interest earned on an initial amount of money (the principal) is added to the principal itself, so that from that point onward, interest is earned on the new, larger principal. In other words, with compound interest, you earn interest not only on your original investment but also on the accumulated interest from previous periods. This effect causes the investment to grow at an accelerating rate over time. Here's how it works: Suppose you invest $1,000 at an annual interest rate of 5%, compounded yearly. After the first year, you earn $50 in interest, making your total $1,050. In the second year, you earn 5% interest on $1,050, which is $52.50, and your total becomes $1,102.50. This process repeats, with the interest each year being calculated on the growing total, leading to exponential growth. Compound interest is widely used in savings accounts, loans, mortgages, and investments. The more frequently the interest is compounded (e.g., monthly, quarterly), and the longer the money remains invested, the greater the effect of compounding. This is why starting to invest early and allowing earnings to compound over time can significantly increase wealth.