Legal Definitions - compound interest

Compound interest is the interest calculated not only on the initial amount of money (the principal) but also on the accumulated interest from previous periods. Essentially, it's 'interest on interest.' This means that as time passes, the interest itself starts earning interest, leading to a faster growth in the total amount of an investment or a more rapid increase in the total amount owed on a debt. It stands in contrast to simple interest, where interest is only calculated on the original principal amount.

• Savings Account Growth: Imagine someone deposits $10,000 into a high-yield savings account that offers a 3% annual interest rate, compounded monthly. In the first month, interest is calculated on the initial $10,000. This small amount of interest is then added to the principal. In the second month, the 3% interest is calculated on the slightly larger sum (original $10,000 plus the first month's interest). This process continues, meaning that each month, the interest earned is based on a slightly larger balance, causing the total savings to grow more quickly over time than if interest were only calculated on the initial $10,000.

• Student Loan Accumulation: Consider a student who takes out a $40,000 loan for their education, and the loan accrues interest at 6% annually, compounded semi-annually, while they are still in school and not making payments. After the first six months, interest is calculated on the $40,000 and added to the loan balance. For the next six months, the interest is then calculated on this new, slightly larger balance (original principal + first six months' interest). This means that by the time the student graduates and starts making payments, the total amount they owe will be significantly more than the original $40,000, not just due to the initial interest, but because that interest itself has been earning further interest.

• Retirement Investment: A young professional invests $200 per month into a retirement fund that typically yields an average annual return of 8%, compounded annually. In the early years, the growth might seem modest. However, after several decades, the fund's value will have grown dramatically. This is because the returns earned each year are reinvested and become part of the principal for the next year's calculation. The interest earned in year 5, for instance, starts earning interest itself in year 6, and this effect multiplies over 30 or 40 years, demonstrating the powerful long-term impact of compound interest on wealth accumulation.