Final answer:
To determine how much more Alexx will have than Spenser after 30 years, we use the compound interest formula with Alexx's yearly return of 5% and Spenser's 4.75% return after the retirement fund fee. Subtracting Spenser's future investment value from that of Alexx gives us the difference in their investments due to the power of compound interest.
Step-by-step explanation:
The question asks us to calculate the amount more Alexx will have than Spenser after 30 years given that both invest $5,000 in the same stock but Alexx invests directly earning 5% a year, while Spenser uses a retirement fund which charges a 0.25% fee, thus earning 4.75% annually. This scenario utilizes the concept of compound interest over a long term.
To calculate the future value of the investments, we use the compound interest formula FV = P(1+r/n)^(nt), where FV is the future value, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years. For Alexx, the future value will be FV = $5,000(1+0.05/1)^(1\*30), and for Spenser, it will be FV = $5,000(1+0.0475/1)^(1\*30).
Once we get the future value for both Alexx and Spenser, we subtract Spenser's future value from Alexx's to find out how much more Alexx has. The calculation would show that Alexx, who avoids the retirement fund fee, ends up with a significant amount more over 30 years due to the power of compound interest.