Evidence That the Rate of Zakah is 2.5%
Question

When and who had decided the percentage (2.5%) of Zakah? Please give reference to the Quran or Hadith.
Praise be to Allah.Reference to the rate of zakah in the Sunnah
The authentic Sunnah states that the zakah on gold and silver is one quarter of one tenth, i.e., 2.5%. A similar rate applies to trade goods and currency nowadays.
Al-Bukhari (1454) narrated from Anas (may Allah be pleased with him) that Abu Bakr (may Allah be pleased with him) wrote to him this document when he sent him to Bahrain: “This is the obligatory charity that the Messenger of Allah (blessings and peace of Allah be upon him) enjoined upon the Muslims and that Allah enjoined upon His Messenger:… for silver, one quarter of one tenth.” 
Abu Dawud (1572) narrated from ‘Ali (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “If you have two hundred dirhams and one full year has passed, then five dirhams are due on them. You do not have to pay anything - i.e. on gold -- unless you have twenty dinars; if you have twenty dinars and one full year has passed, then half a dinar is due on them, and if the number increases then work it out on this basis.” (Classed as sahih by al-Albani in Sahih Abi Dawud)
Ibn Majah (1791) narrated from Ibn ‘Umar and `Aishah (may Allah be pleased with them both) that the Prophet (blessings and peace of Allah be upon him) used to take from every twenty dinars or more, half a dinar, and from forty dinars, one dinar. (Classed as sahih by al-Albani in Sahih Ibn Majah) 
Ibn Abi Shaybah narrated in al-Musnad (9966) with a good chain of transmission from ‘Ali (may Allah be pleased with him) that he said: “Nothing is due on anything less than twenty dinars; for twenty dinars, half a dinar is due; for forty dinars, one dinar is due. For anything more than that, it is to be worked out.” (Irwa al-Ghalil, 3/291) 
These hadiths indicate that the zakah on gold and silver is 2.5%, and there is scholarly consensus on this point. 
It says in al-Mawsu‘ah al-Fiqhiyyah (21/29-30): 
“The jurists unanimously agreed that the threshold for gold at which zakah becomes due is twenty dinars. When it reaches that amount, one quarter of one tenth should be paid on it.”
It says in Fatawa al-Lajnah al-Daimah: 
“What is required is to pay one quarter of one tenth on what you have of gold or silver or currency or trade goods, if all of that reaches the minimum threshold by itself or when added to whatever you have of other wealth that is subject to zakah, whether it is money or trade goods, and one year has passed.” (Fatawa al-Lajnah al-Daimah, 9/439) 
When was zakah made obligatory? 
With regard to when the obligatory duty of zakah began, that was in Makkah before the Hijrah, then from the second year AH the definition of the rates and the detailed rulings were established. 
Hence some scholars say that zakah was made obligatory in the second year AH. 
Ibn Kathir (may Allah have mercy on him) said: 
“It is not far-fetched to say that the principle of obligatory charity (zakah) was enjoined at the beginning of the Prophet’s mission, as in the verse (interpretation of the meaning): “but pay the due thereof on the day of their harvest” [al-An'am 6:141]. As for the zakah in which there is a minimum threshold and set rates, that was introduced in Madinah.”
He also said: 
“The obligation of zakah came in the second year AH in Madinah, according to what was stated by more than one.” (Tafsir Ibn Kathir, 7/164) 
Al-Haytami said in Tuhfat al-Muhtaj (3/209): 
“The obligation to pay zakah on one’s wealth came in the second year AH, after sadaqat al-fitr was introduced.”
In Hashiyat al-Bujayrami ‘ala al-Khatib (2/313) it says: “
With regard to the words “was enjoined in the second year”, there was a difference of opinion as to which month that happened in. What was stated by our shaykh al-Babili is that the most well-known view of the hadith scholars is that it was enjoined in Shawwal of the year mentioned.” (See: Asna’l-Matalib, 4/175; Kashshaf al-Qina’, 2/166) 
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said: 
“Zakah was enjoined, according to the soundest opinion of the scholars, in Makkah, but the definition of the minimum threshold and types of wealth on which zakah is due, and who is entitled to zakah, came in Madinah.” (Majmu‘ Fatawa Ibn ‘Uthaymin, 13/1357) 
For more, please see this category: Conditions for Zakah Being Obligatory
And Allah knows best.