Final answer:
The problem involves calculating the future value of $5,000 investments for Alexx and Spenser over 30 years, with different annual interest rates due to a management fee. The future value for both investments is determined using the compound interest formula, and the difference is found by subtracting Spenser's future value from Alexx's.
Step-by-step explanation:
The question requires us to calculate the future value of investments for Alexx and Spenser after 30 years, with Alexx earning 5% interest and Spenser earning an effective 4.75% interest due to a 0.25% management fee. To find out how much more Alexx will have than Spenser after 30 years, we need to use the formula for compound interest:
Future Value = Principal × (1 + interest rate)^number of periods
For Alexx: Future Value = $5,000 × (1 + 0.05)^30
For Spenser: Future Value = $5,000 × (1 + 0.0475)^30
We can calculate these two values and then subtract Spenser's future value from Alexx's to determine the difference between their investments.