# Answer to Question #71396 in Microeconomics for Jane

Question #71396

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?

I have no clue on how to do this problem and I am in tears

I have no clue on how to do this problem and I am in tears

Expert's answer

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%.

We should use compound interest formula: A = P*(1 + r)^t.

After 30 years Alexx will have: A1 = 5,000*(1 + 0.05)^30 = $21,609.71,

After 30 years Spenser will have: A2 = 5,000*(1 + (0.0475 - 0.0025))^30 = $18,726.59,

A1 - A2 = $21,609.71 - $18,726.59 = $2,883.12

So, Alexx will have $2,883.12 more than Spenser.

We should use compound interest formula: A = P*(1 + r)^t.

After 30 years Alexx will have: A1 = 5,000*(1 + 0.05)^30 = $21,609.71,

After 30 years Spenser will have: A2 = 5,000*(1 + (0.0475 - 0.0025))^30 = $18,726.59,

A1 - A2 = $21,609.71 - $18,726.59 = $2,883.12

So, Alexx will have $2,883.12 more than Spenser.

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