Compound Interest

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. This means that interest is earned on interest, leading to exponential growth over time. Understanding how compound interest works is crucial for both investing and borrowing, as it can significantly affect the growth of investments and the cost of loans. # What is Compound Interest? ## Definition Compound interest is the process of earning interest on both the original amount of money (the principal) and on the interest that has previously been added to the principal. This results in interest being calculated on an increasingly larger amount over time. ## Basic Formula The formula for compound interest is: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) = the future value of the investment/loan, including interest - \( P \) = the principal investment amount - \( r \) = the annual interest rate (decimal) - \( n \) = the number of times interest is compounded per year - \( t \) = the number of years the money is invested or borrowed for # How Compound Interest Works ## Compounding Frequency Interest can be compounded on different schedules, such as annually, semi-annually, quarterly, monthly, or daily. The more frequently interest is compounded, the greater the amount of compound interest will be. ### Example If you invest $1,000 at an annual interest rate of 5% compounded annually for 5 years, the future value can be calculated as: \[ A = 1000 \left(1 + \frac{0.05}{1}\right)^{1 \times 5} = 1000 \left(1.05\right)^5 \approx 1276.28 \] ## Benefits of Compound Interest ### Growth Over Time The power of compound interest lies in its ability to grow investments significantly over time. Even small contributions can grow substantially with regular compounding. ### Investing and Saving Regularly investing or saving with compound interest can lead to significant wealth accumulation. For example, consistent contributions to a retirement account benefit greatly from compound interest. # Conclusion Compound interest is a powerful financial concept that can greatly enhance the growth of investments or increase the cost of loans over time. By understanding how compound interest works and leveraging its potential, individuals can make more informed decisions about saving, investing, and borrowing.