Οὕτως γὰρ ἠγάπησεν ὁ θεὸς τὸν κόσμον ὥστε τὸν υἱὸν αὐτοῦ τὸν μονογενῆ ἔδωκεν ἵνα πᾶς ὁ
πιστεύων εἰς αὐτὸν μὴ ἀπόληται ἀλλ᾽ ἔχῃ ζωὴν αἰώνιον - Jn 3:16
Biblical greek was not as completely understood in the past (e.g. Wycliffe, Tyndale, KJV era) as much as it has been in the recent past.
πιστεύων εἰς αὐτὸν is commonly translated "believes in Him," and down through the centuries, this singular interpretation has taken hold due to familiarity and tradition. Modern translators find it extremely difficult to break from tradition as well and they continue to provide this familiar translation, especially when it comes down to pivotal verses such as John 3:16. Why? In fear of condemnation of overturning centuries of church tradition and doctrine (translation sales are also not far from sight too, I'm sure).
TDNT, Liddell's, etc. today now admit that πιστεύω (pisteuo) includes the meanings "obey," "obedience," "comply," and "trust". The word εἰς (eis), as those dictionaries and lexicons agree, is more properly translated "for" or "unto". The only time eis has the meaning "in" is when the verb it modifies is a verb of motion - pisteuo is not. On the other hand, the presence of "eis" also modifies the verb it is attached to - in this case, it precludes the possibility that "pisteuo" simply means "believe"!
Secondly, the πιστεύων is in the Greek present participle active, which implies something which is continuous and persistent.
In essence and conclusion, the meaning of John 3:16 is more precisely:
"For Elohim so loved the world that He gave His only begotten Son, that everyone who
keeps on trusting and obeying Him may not perish, but may have eternal life."
John 3:36 has the same Greek grammar. It translates, according to the same rules, more precisely: "He who
keeps on trusting and obeying the Son has eternal life ..."