TITLE: How would multiplying money work?
QUESTION [13 upvotes]: This is a very silly question since nobody will actually do this because it makes very little sense in the real world but I just want to know how would it actually work if possible.
For example let us take an amount of 2 dollars and 2 cents and multiply that buy 2 dollars and 2 cents. Would the result be 4 dollars and 4 cents? The only way to make sense out of this for me is to treat them as vectors and multiply components.

REPLY [2 votes]: Squaring an amount of money could reflect a long-term investment plan. Assume that you invest an amount $x$ and you wonder "what should be the yearly return so that I will have $x^2$ in $n$ years?", if I leave principal and interest intact for the duration?
You're young, say 20, and you think, "let's forget USD 100 for the next 40 years. What would it take to make them USD 10,000?"
Solving
$$100\cdot (1+r)^{40} = (100)^2 \implies r \approx 12.20 \%$$
Hmmm, rather large for a yearly real  interest rate (inflation subtracted), averaged over 40 years-this is probably why squaring a monetary sum is not frequently encountered. You could get something like $r= 6\%$, and you will need $72$ years to reach $10,000$. So start when you're born.
But it may be the case that you are a risk-loving (or risk-seeking) individual, in which case your utility function with respect to wealth would be convex - and
$$u(W) = W^2$$
is as good as any.