Final answer:
To compare the final value of Alexx and Spenser's investments after 30 years, the future value formula is applied to both scenarios, taking into account the different annual interest rates due to the administrative fee Spenser pays.
Step-by-step explanation:
Comparing Retirement Investment Growth
The question involves comparing the investment growth of two individuals, Alexx and Spenser, over a 30-year period.
Alexx invests $5,000 directly earning 5% annually without any administrative fees, while Spenser invests the same amount but through a retirement fund that charges a 0.25% fee, resulting in an annual earning rate of 4.75%.
To calculate the future value for both investments, we use the future value formula:
FV = P × (1 + r)^n, where FV is the future value, P is the principal amount, r is the annual interest rate, and n is the number of years.
For Alexx, P = $5,000, r = 5% or 0.05, and n = 30 years. For Spenser, P stays at $5,000, but r = 4.75% or 0.0475 due to the administrative fee.
Calculating for both:
- Alexx's investment: FV = $5,000 × (1 + 0.05)^30
- Spenser's investment: FV = $5,000 × (1 + 0.0475)^30
We subtract Spenser's future value from Alexx's future value to determine how much more Alexx will have than Spenser after 30 years.