Commercial sense of "an investing of money or capital" is from 1610s, originally in reference to the East India Company; general use is from 1740 in the sense of "conversion of money to property in hopes of profit," and by 1837 in the sense "amount of money invested." For evolution of the commercial senses, see invest.
The sense development from "highest" to "total number, the whole" probably is via the Roman custom of adding up a stack of figures from the bottom and writing the sum at the top, rather than at the bottom as now (compare the bottom line).
General sense of "numerical quantity" of anything, "a total number" is from late 14c. Meaning "essence of a writing or speech" also is attested from mid-14c. Meaning "aggregate of two or more numbers" is from early 15c.; sense of "arithmetical problem to be solved" is from 1803. Sum-total is attested from late 14c., from Medieval Latin summa totalis.
late 14c., "interchangeable," from Old French convertible "interchangeable" (13c.) and directly from Late Latin convertibilis "changeable," from Latin convertere "to turn around; transform," from assimilated form of com "with, together" (see con-) + vertere "to turn" (from PIE root *wer- (2) "to turn, bend").
Meaning "capable of being changed in form, substance, or condition" is from 1530s. Of paper money, etc., "capable of being converted into gold of a similar amount," from 1834. The noun is recorded from 1610s; meaning "automobile with a fold-down top" is from 1916. Related: Convertibility.
"wealthy, affluent, having money," mid-15c., from past participle of Middle English verb moneien "to supply with money" (see money (n.)).