What Is Interest on Interest and How Does It Work?

The Concept of Compound Interest

Compound interest, often referred to as “interest on interest,” represents a financial principle where earnings are generated not only on the initial principal but also on accumulated interest from preceding periods. This mechanism contrasts with simple interest, which calculates earnings solely on the original principal. Previously earned interest itself begins to earn interest, leading to a snowball effect on growth or cost over time. This effect can accelerate wealth accumulation for savers and investors, while also increasing the total cost for borrowers.

The interest rate plays a direct role, as a higher rate leads to faster growth of both principal and accumulated interest. The frequency of compounding dictates how often interest is calculated and added back to the principal. Interest can be compounded at various intervals, such as annually, semi-annually, quarterly, monthly, or even daily. More frequent compounding means interest is added more often, allowing it to start earning its own interest sooner and resulting in higher overall returns compared to less frequent compounding at the same annual rate.

How Compound Interest is Calculated

The standard formula to determine the future value of an investment or loan with compound interest is A = P(1 + r/n)^(nt). In this formula, ‘A’ represents the future value, including interest. ‘P’ stands for the principal investment amount. The variable ‘r’ denotes the annual interest rate, expressed as a decimal.

The frequency of compounding is represented by ‘n’, which is the number of times interest is compounded per year. For instance, if interest is compounded monthly, ‘n’ would be 12, while quarterly compounding means ‘n’ is 4. Finally, ‘t’ signifies the number of years the money is invested or borrowed for.

To illustrate, consider an initial principal of $1,000 invested at an annual interest rate of 5%, compounded annually for three years. In the first year, interest earned is $1,000 0.05 = $50. This $50 is added to the principal, making the new balance $1,050 for the start of the second year. For the second year, interest is calculated on this new balance: $1,050 0.05 = $52.50.

The interest from the second year, $52.50, is added to the $1,050, resulting in a balance of $1,102.50 for the third year. In the third year, interest is calculated on $1,102.50, yielding $1,102.50 0.05 = $55.13. After three years, the total accumulated amount would be $1,102.50 + $55.13 = $1,157.63.

Common Applications of Compound Interest

Savings accounts and certificates of deposit (CDs) frequently utilize compounding, where interest earned is periodically added back to the principal. The frequency of compounding can vary, commonly ranging from daily to quarterly.

Loans and mortgages also operate on a compound interest basis, impacting the total amount repaid by borrowers. Interest accrues on the outstanding principal balance, and if any interest from previous periods remains unpaid, it can be added to the principal, leading to interest being charged on that unpaid interest as well. Early payments on the principal can significantly reduce the total interest paid over the life of the loan.

Credit cards are another common example where compound interest plays a substantial role. When a balance is carried over from one billing cycle to the next, interest is charged on the outstanding amount. This outstanding balance includes original purchases, previously unpaid interest, and fees. If the full balance is not paid off, interest can compound quickly, increasing the total debt owed.

When investors reinvest dividends, capital gains, or other earnings from stocks, bonds, or mutual funds, those reinvested amounts become part of the principal. This larger principal then generates its own returns, which can also be reinvested, creating a compounding cycle that enhances investment growth over extended periods.