HaPnida or HaMnida?

There are tons of Korean phrases that end with ‘합니다’ – 감사합니다 (thank you), 미안합니다 (I am sorry), 사랑합니다 (I love you), and so on. But some people wonder;

Why 합니다 [haP-ni-da] sounds like 함니다[haM-ni-da]?
Which one is correct? 합니다 with ‘ㅂ’ or 함니다 with ‘ㅁ’?
The truth is both of them are correct in some sense.

합니다
with ‘ㅂ’ is the way it should be written. and

함니다
with ‘ㅁ’ is the way it should be pronounced.

There is one Korean pronunciation rule called nasalization (비음화) and basically the rule states that when a non-nasal sound (‘ㅂ’ in this case) meets a nasal sound (‘ㄴ’ in this case), the non-nasal character changes its sound value to a nasal sound (‘ㅁ’ in this case – both ‘ㄴ’ and ‘ㅁ’ are nasal sounds). Hence, 합니다 will sound like 함니다. – For more information on this rule please check out the video lesson.

Source: busyatom