Compound interest is the interest on a loan or deposit that's calculated based on both the initial principal and the accumulated interest from previous periods. Unlike simple interest, where interest is calculated solely on the principal amount, compound interest calculates interest on the initial amount and also on the accumulated interest.

To understand compound interest, consider an example: If you deposit $1,000 in a bank account that offers an annual interest rate of 5%, and that interest is compounded annually, after the first year, you'll earn $50 in interest, making your total $1,050. In the second year, the bank will compute the interest not just on your initial $1,000 deposit, but on the full $1,050. So, you'll earn $52.50 in interest for the second year, making your total $1,102.50. As years go by, this process repeats, and the amount by which your investment grows becomes larger, all thanks to the interest being calculated on an increasingly larger base amount.

The frequency with which interest is compounded plays a significant role in how much interest accumulates. It can be compounded annually, semi-annually, quarterly, monthly, or even daily. The more frequently interest is compounded, the more the total amount grows.

The magic of compound interest comes into play particularly with long-term investments. Over time, the compounding effect can lead to exponential growth of the principal amount, especially if the interest is compounded frequently. This principle is why financial advisors often stress the importance of starting savings and investments early, as given enough time, compound interest can significantly boost the value of savings and investments.