when someone offers to sell you something, if you buy it then I would say you wanted it
the market price is what shows in a quote of the stock, just the way you normally track the present value of your investime 2.04 one day, 5.62 some other day
It is really not rock science.
If you bought 100 shares at 2.04 originally, and they now have a market price of 4.47 then you are up over 100%
If you want to buy all that the rights offering allows for you then you would be buying 10 shares at 2.24 each
So your average cost would go up from 2.04 to around 2.06, but you would get 10 shares for half of the current market price (2.24 instead of 4.47)
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