Economics help

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I have no idea how they came to this formula, because I see it a totally different way. I understand the entire theory behind it. it's simple, but their formula is ass backwards in my mind

x = 100 / (1.05)30 and apparently it equals 23.14 somehow. That formula is to find how much money you would need to invest to get 100 dollars after 30 years

Widow, I'm no mathematician, but one factor omitted is whether the interest is compounded, and if so, at what period. In other words, if interest is compounded quarterly, principle of one hundred dollars at, say, ten percent per annum would mean that after the first quarter, the principle would become $102.50 instead of an even hundred dollars. I've heard that in some situations, interest can be compounded to the principle on a daily basis.

It seems to me you are assuming that the interest would only be compounded annually.

Don't understand a lot of the terms used, but it should be [starting money] = [end result] / ( ( [interest rate] + 1 ) ^ [years to wait] ), or in this case, x=100/(1.05^30)

Think of it this way.
1.05^30 = 4.322
100/4,322= $23.14

In other words, if you invested $23.14 into something, and let it sit there and make a constant 5% each year, you'd have $100 after 30.

Or:
Year 0: $23.14
Year 1: $23.14 * 1.05
Year 2: $23.14 * 1.05 * 1.05 = $23.14 * (1.05^2)
Year n: $23.14 * (1.05^n)