Final answer:
After 30 years of investing, Alexx, who invests directly and earns a 5% return, will have $633.20 more than Spenser, who uses a retirement fund with a 4.75% return after deducting an administrative fee.
Step-by-step explanation:
The question involves the calculation of the future value of investments for Alexx and Spenser with different annual returns, taking into account a small administrative fee for Spenser's investment through a retirement fund. To calculate the future value for both Alexx and Spenser, we use the formula for the future value of an investment, which is FV = P * (1 + r)^n, where FV is the future value, P is the initial investment, r is the annual interest rate, and n is the number of years.
For Alexx: FV_Alexx = 5000 * (1 + 0.05)^30
For Spenser: FV_Spenser = 5000 * (1 + 0.0475)^30
Next, we calculate the difference between the two future values to see how much more Alexx has than Spenser after 30 years.
After calculations:
Difference: $633.20
Alexx will have $633.20 more than Spenser after 30 years due to the difference in the net return resulting from the administrative fee charged to Spenser.