Dr. Zakir Naik: Allah says in the Quran in Surah Baqara ch. 2 verse 184 that

"If it is difficult for a person to fast he can either fast or he can give a ransom that is feeding of a poor person"

As far as those elderly person who exempted are those people whose health is so weak that if they fast it will damage their health. A person whose reached a very elderly age the age is not fixed whether it is 60 or 70 or 80 or 90 depending upon health condition, due to the old age if his health condition is bad which prevents him from fasting then is the time where he should feed one indigent person.

And there is a hadith of our beloved Prophet Muhammad(saws), Sahih Bukhari Vol. 6 hadith no. 4505 where beloved Prophet said that

"The old elderly men and women they need not fast but they have to feed one poor person for every fast they skip"

And similarly there are various hadith's for e.g.

if you read Daara Qutni wol. 2 hadith no. 208 it says that

"If a person who has to give a ransom he has to feed a poor person one mud of wheat, one mud is equal to two hands of stretched full of wheat that is what you should feed.

There is another hadith which says in Daara Qutni hadith no. 270 that Anas (may Allah be pleased with him) one year when he became very old and he could not fast so at the end of the month he called thirty poor people and he fed them with bread crums and meal...aaa.. Proper meal for thirty poor people. So it mean that for every fast you miss you should feed one poor person but coming back to the question that if the elderly person is of sound mind and not healthy that's the time he has to feed a person or give the ransom but if a person is elderly and he becomes insane, if he's not of sound mind then he doesn't have to fast he's exempted neither does he has to give any ransom neither he has to compensate, because he's like a child as our beloved Prophet said earlier which I mentioned.