Final answer:
To determine how much more Alexx will have than Spenser after 30 years, we use the compound interest formula to calculate the future value of both investments and then subtract Spenser's future value from Alexx's future value.
Step-by-step explanation:
The question is asking us to calculate how much more money Alexx will have compared to Spenser after 30 years of investing $5,000 in the same stock with slightly different annual returns due to administrative fees charged by the retirement fund used by Spenser.
To calculate the future value of an investment, we use the formula for compound interest: Future Value = Principal × (1 + rate)^n, where Principal is the initial amount invested, rate is the annual interest rate, and n is the number of years the money is invested.
For Alexx, the calculation is $5,000 × (1 + 0.05)^{30} and for Spenser $5,000 × (1 + 0.0475)^{30}.
After performing these calculations:
Alexx's investment value: $5,000 × (1.05)^{30}
Spenser's investment value: $5,000 × (1.0475)^{30}
To find out how much more Alexx will have than Spenser after 30 years, we subtract Spenser's future value from Alexx's future value.