Question

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

Answer 1

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.