Present Perfect: Endings

Bear in mind that this tense is called [present] perfect because we can see (now, in the present) the result of what has been perfected, done, carried out, achieved.

Philip sees a hare and lets the dog off the lead:
ὁ μὲν Φίλιππος λαγὼ ὁρᾶ, λύει οὖν τὸν κύνα.
Now Philip has let the dog go, see Argos running after the hare.
ὁ Φίλιππος ἤδη λέλυκε τὸν κύνα, ὅρα τὸν Ἀργὸν μετὰ τὸν λαγὼ τρέχοντα.

Compare the personal endings
 
Active Voice
Present      Perfect
loosens  Who  has loosened
 λύ ω   I   λέλυκ α 
 λύ εις   you (sg)   λέλυκ ας 
 λύ ει   he/she/it   λέλυκ ε (ν)
 λύ ομεν   we   λελύκ αμεν 
 λύ ετε     you (pl)   λελύκ ατε 
 λύ ουσιν   they   λελύκ ασιν 
   
Middle/Passive Voice
Present      Perfect
is loosened  Who  has been loosened
 λύ ομαι   I   λέλυ μαι 
 λύ [εσαι] ῃ    you (sg)   λέλυ σαι 
 λύ εται   he/she/it   λέλυ ται (ν)
 λύ ομεθα   we   λελύ μεθα 
 λύ εσθε     you (pl)   λέλυ σθε 
 λύ ονται   they   λέλυ νται 
 

Active Voice κ inserted between stem and thematic vowel, α in all endings except 3rd person singular (he-she-it) which takes an ε and a movable ν if followed by a punctuation mark or by a word beginning with a vowel or a diphthong.

Middle/Passive Voice: Endings attached directly to the stem, no thematic vowel (ο/ε) between the stem and the ending. As is the case in the Present Tense.