Compound interest is a financial concept that refers to the interest calculated on the initial principal, which also includes all the accumulated interest from previous periods on a deposit or loan. In other words, it's interest on interest, and it can lead to exponential growth of a sum of money over time.

The formula for compound interest is given by:
\[A = P \left(1 + \frac{r}{n}\right)^{nt}\]
where:
- \(A\) is the future value of the investment/loan, including interest.
- \(P\) is the principal amount (initial investment or loan amount).
- \(r\) is the annual interest rate (in decimal form).
- \(n\) is the number of times that interest is compounded per year.
- \(t\) is the time the money is invested or borrowed for, in years.

The compound interest formula takes into account the compounding periods per year. The more frequently interest is compounded, the more interest accrues on the initial principal, resulting in higher overall returns or debt accumulation. Compound interest is widely used in various financial contexts, such as savings accounts, investments, loans, and mortgages.

Compound interest refers to the interest earned on both the principal amount and the accumulated interest on that amount over a period of time. In simple terms, it means that the interest earned on an investment is reinvested to earn additional interest in the subsequent periods, leading to exponential growth of the investment. Compound interest is a powerful tool for wealth creation and is used extensively in the financial industry.

The concept of compound interest can be better understood by looking at an example. Let's assume that you invest $10,000 for 10 years at an annual interest rate of 5%. The interest earned in the first year would be $500, and the new principal amount would be $10,500. In the second year, the interest earned would be calculated on the new principal amount, which is $10,500, resulting in interest of $525. This process continues over the 10-year period, resulting in a total interest of $6,386.93 and a final amount of $16,386.93. Thus, the power of compound interest is evident in this example, where the interest earned on the investment is reinvested to earn additional interest, resulting in a significantly higher return on investment.

Compound interest can be calculated using the formula A = P(1+r/n)^nt, where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the number of years. The formula can be used to calculate the interest earned on any investment that earns compound interest.

The frequency of compounding can have a significant impact on the interest earned on an investment. The more frequently the interest is compounded, the higher the interest earned. For example, if an investment earns 5% interest annually and is compounded once a year, the interest earned in the first year would be $500. However, if the interest is compounded quarterly, the interest earned in the first quarter would be $125, resulting in a total interest of $6,385.62 over 10 years, which is slightly higher than the interest earned with annual compounding.