Final answer:
To find out how much more Alexx will have than Spenser after 30 years, we must calculate the future value of their investments considering their respective interest rates and subtract Spenser's final amount from Alexx's final amount.
Step-by-step explanation:
The question involves calculating the future value of investments for Alexx and Spenser, who each start with an initial investment of $5,000. The difference is due to the charging of an administrative fee by the retirement fund used by Spenser. To determine the difference in their investment's worth after 30 years, we use the formula for compound interest: A = P(1 + r/n)^(nt), where:
- P is the principal amount ($5,000)
- r is the annual interest rate (0.05 for Alexx, 0.0475 for Spenser)
- n is the number of times that interest is compounded per year
- t is the time the money is invested for (30 years)
Assuming the interest is compounded annually, Alexx's investment grows as follows:
A = 5000(1 + 0.05)^30 = 5000(1.05)^30.
Spenser's investment, after the 0.25% fee, grows as follows:
A = 5000(1 + 0.0475)^30 = 5000(1.0475)^30.
We then subtract Spenser's final amount from Alexx's final amount to find the difference:
Difference = (5000(1.05)^30) - (5000(1.0475)^30).
Using a calculator, we find the exact difference in dollars and cents to answer the question about how much more Alexx will have than Spenser after 30 years.