When you think of the percent symbol, people tend to rely on the slash mark preceded with a superscript 'o' (or a degree symbol °), and followed by a subscript degree symbol (or baseline lowercase 'o'). It seems logical that the symbol for cents would also contain a slash instead of a vertical line through it. The majority of fonts on my computer still contain the proper way to symbolize a ¢ mark with a forward solidus. You see wiki's reference to currency symbols at Currency Symbols table with international variations.
this URL† will explain a bit more about the American cent, but notice that the former link has a symbol of a capital letter C with a double stroke of forward solidus marks. Although the US dollar sign can be used with a single stroke as well as a double stroke, the ₡ (colón) symbol is only used in Central American countries like El Salvador. Incidentally, the "Character Palette" feature on my Mac describes this symbol simply as a colon sign, which might seem quite insulting if used in a sentence for exchanging either services or merchandise. English has always had a rude disregard for accent marks.
Before I did a quick search on the Internet, I always thought a cent symbol could be interchanged with a capital c with a (vertical) line through it, and the ¶ (pilcrow") was a reverse 'P' with a double stroke stem. Wrong again! Apparently the pilcrow symbol developed from a capital letter 'C' which was the abbreviation for the word Capitulum. Are you sleeping yet? This is important because stereotyping symbols used to designate words in the spoken language could end up in a disaster like selling stocks & bonds for ass. Maybe I'm a bit dyslexic because I recall a time when I believed the ¶ sign was a capital letter 'P' with a double stroke stem (i.e. ⁋). I love learning `bout the history of symbols and special characters of the alphabet because it gives me freedom to design my own character when dabbling in calligraphy.