There is a much simpler way to think about the math.

Multiplication is commutative--that means it doesn't matter what order you multiply a bunch of numbers together. 2*3*5*7 = 3*5*7*2 = 7*2*3*5 and so on.

When you invest a chunk of money in the stock market, it basically multiplies each year. On average, it multiplies by somewhere around 1.1. A front load of 5.75% adds one initial multiplier of 0.9425. But, as you know, even small investments turn into fuck gobs of money over 30+ years. And since multiplication is commutative, an initial 5.75% penalty is equivalent to no initial penalty, followed by a 5.75% penalty on your fuck gobs. This is bad.

However, we can ask a more interesting question. Money managers charge these fees because, in theory, their investment choices give higher returns. So how much more profitable than the market would the manager have to be to justify his 5.75% fee?

Investing P dollars every year for n years at rate of return r has a final value of:

P(r^n-1)/(r-1)

Doing the same with a up-front multipler of f (so, for your 5.75% fee f=0.9425) has a final value of:

fP(r^n-1)/(r-1)

So assuming we can earn 10% from the market each year and the manager charges a front load fee of f, what returns does the manager have to earn to break even with his fee?

(1.1^n-1)/(1.1-1) = (r^n-1)/(r-1) * f

Which, for n=30 gives the somewhat surprising answer r=1.103. (

http://www.wolframalpha.com/input/?i=%28r%5E30+-+1%29%2F%28r-1%29+%3D+%281.1%5E30-1%29+%2F+0.1+%2F+0.9425) So, if the manager's average yearly returns are even half a percent better than the market's, his front-load fee is actually worth it!

High expense ratios are actually the much bigger problem. Very simply, to be justified, the manager must beat the market by the amount his expense ratio exceeds Vanguard's (basically the whole thing). So, interestingly, it is much easier for the manager to justify the scary-looking front load than it is to justify the 1.4% ERs!

Whether any money managers actually achieve these goals, and whether they can be identified, is a much tougher question to answer, but many wise mustachians will advise no.