Final answer:
After 30 years, Alexx, who invested directly and earned 5% a year, will have $652.88 more than Spenser, who invested through a retirement fund earning 4.75% a year after a 0.25% fee.
Step-by-step explanation:
To calculate how much more Alexx will have than Spenser after 30 years given their investment strategies and rates of return, we use the formula for compound interest:
A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
Assuming the interest is compounded once per year (n=1), we get:
For Alexx: Alexx's final amount = 5000(1 + 0.05/1)^(1*30) = $21646.57
For Spenser, taking into account the 0.25% management fee: Spenser's final amount = 5000(1 + (0.0475 - 0.0025)/1)^(1*30) = $20993.69
The difference between Alexx's and Spenser's final amounts is: $21646.57 - $20993.69 = $652.88.
Therefore, after 30 years, Alexx will have $652.88 more than Spenser.