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Many retirement funds charge an administrative fee each year equal to 0.25% on managed assets. Suppose that Alexx and Spenser each invest $5,000 in the same stock this year. Alexx invests directly and earns 5% a year. Spenser uses a retirement fund and earns 4.75%. After 30 years, how much more will Alexx have than Spenser?

a) $62.50
b) $250
c) $5,000
d) $10,000

1 Answer

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Final answer:

After 30 years, using the compound interest formula, Alexx's investment will grow to $21,610.27, while Spenser’s investment will grow to $20,777.09. The difference is $833.18, but this option is not provided in the choices. Thus, it suggests a potential error in the provided choices or the question details.

Step-by-step explanation:

The question involves calculating the future value of investments for Alexx and Spenser, given that they both start with a $5,000 investment. Alexx's investment grows at a 5% annual rate, while Spenser's investment grows at a 4.75% annual rate, due to a 0.25% administrative fee charged by the retirement fund. To find out how much more Alexx will have than Spenser after 30 years, we will use the compound interest formula which is A = P(1 + r/n)^(nt).

For Alexx:
A = $5,000(1 + 0.05)^30
A = $5,000(1.05)^30
A = $21,610.27 (rounded to two decimal places)

For Spenser:
A = $5,000(1 + 0.0475)^30
A = $5,000(1.0475)^30
A = $20,777.09 (rounded to two decimal places)

The difference between Alexx’s and Spenser's investments after 30 years is:
$21,610.27 - $20,777.09 = $833.18.

However, since the provided options do not include this answer, and assuming no further contributions were made to these funds, there seems to be a calculation error or a misunderstanding with the question's numbers. In such cases, it would not be appropriate to select an answer from the provided choices as none of them match the calculation.

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