Define compound interest as explained in LifeX materials.

Compound interest is defined as the interest that is calculated not only on the initial principal but also on the accumulated interest from previous periods. This means that as interest is added to the principal, the new total becomes the basis for calculating future interest. This cumulative effect allows for growth over time, making compound interest a powerful concept in finance and investment.

For example, if you have an account that earns compound interest, each period's interest is calculated based on the total amount in the account, including both the original investment and any interest that has already accrued. This leads to exponential growth, as the interest itself begins to earn interest.

In contrast to other definitions, the option referring to interest calculated only on the initial principal does not capture the growth dynamics of compound interest. Similarly, interest that remains constant over time does not express how compound interest works since it is inherently variable based on the balance, which changes over time. Lastly, interest deducted from savings accounts periodically describes a practice related to account management rather than defining how interest accumulates over time, which is central to understanding compound interest.