Final answer:
After 30 years, the difference in Alexx's and Spenser's investment earnings can be calculated using the compound interest formula. Alexx, investing directly, will have a higher future value than Spenser, who uses a retirement fund with an administrative fee. The calculated difference will indicate how much more Alexx will have than Spenser.
Step-by-step explanation:
The question asks about the difference in earnings between Alexx and Spenser after investing in the same stock with different annual rates due to administrative fees associated with a retirement fund. To calculate the future value of investments for both individuals, we use the formula for compound interest, which is A = P(1 + r/n)^{nt}, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time the money is invested for.
For Alexx, who invests directly without the administrative fee, the future value A is calculated with an annual interest of 5%). For Spenser, the future value is calculated with a slightly lower annual interest rate of 4.75% due to the retirement fund's fee. After 30 years, the difference in their investment's future values can be calculated to determine how much more Alexx will have than Spenser.
- Calculate Alexx's future value using the compound interest formula with P = $5,000, r = 5%, n = 1, and t = 30.
- Calculate Spenser's future value using the compound interest formula with P = $5,000, r = 4.75%, n = 1, and t = 30.
- The difference in the earnings is Alexx's future value minus Spenser's future value, showing how much more Alexx will have than Spenser after 30 years.