Final answer:
Option d illustrates the compounding of interest for Alicia's investment because it shows the investment's value increasing each year due to interest on both the principal and the accumulated interest.
Step-by-step explanation:
To understand which scenario illustrates the compounding of interest over time for Alicia's investment, we should examine each of the options given. The essence of compound interest is that interest is calculated on the initial principal, which also includes all of the accumulated interest from previous periods.
- Option a involves Alicia spending part of her interest each year, which does not allow interest to compound on the interest; this represents a simple interest scenario.
- Option b involves a withdrawal that does not give details about the interest's compounding.
- Option c also describes a simple interest scenario because Alicia receives a fixed amount of interest each year without reinvestment.
- Option d, where Alicia's investment is worth $1,050 after one year and $1,102.50 after two years, shows an increase that accounts for interest on top of the previously earned interest. This is a clear example of compounded interest.
Therefore, option d correctly illustrates the compounding of interest over time because the investment value grows each year not only from the initial principal but also from the interest of previous years.