Does Islam forbid saving up wealth?
Question

                Why does Islam forbid saving up wealth?.
Praise be to Allah.
    Islam does not forbid saving up wealth in all cases, rather 
    what is forbidden and what a stern warning is issued against is not paying 
    zakaah on one’s wealth. But if a person pays zakaah, he is not included in 
    the condemnation.                                      

    Allaah says (interpretation of the meaning): 

    “And those who hoard up gold and silver (Al‑Kanz: the 
    money, the Zakaah of which has not been paid) and spend them not in the way 
    of Allaah, announce unto them a painful torment”

    [al-Tawbah 9:34]

    Abu Dawood (1564) narrated from Umm Salamah (may Allaah be 
    pleased with him) that the Prophet  (peace and blessings of Allaah be 
    upon him) said: “That which reaches the level where zakaah is to be paid and 
    its zakaah is paid, is not kanz (hoarded wealth).” Classed as hasan 
    by al-Albaani in Saheeh Abi Dawood. 

    Al-Bukhaari (1404) narrated that Khaalid ibn Aslam said: We 
    went out with ‘Abd-Allaah ibn ‘Umar (may Allaah be pleased with him) and a 
    Bedouin said: Tell me about the words of Allaah, “And those who hoard up 
    gold and silver (Al‑Kanz: the money, the Zakaah of which has not been paid) 
    and spend them not in the way of Allaah”. Ibn ‘Umar (may Allaah be 
    pleased with him) said: The one who hoards them and does not pay zakaah on 
    them, woe to him. That was before zakaah was revealed; when it was revealed, 
    Allaah made it a purification of wealth. 

    Maalik narrated in al-Muwatta’ (595) that ‘Abd-Allaah 
    ibn Dinar said: I heard ‘Abd-Allaah ibn ‘Umar when he was asked about kanz – 
    what is it? He said: It is wealth on which zakaah is not paid. 

    Ibn Katheer (may Allaah have mercy on him) said commenting on 
    the verse in al-Tawbah: With regard to kanz, Maalik said, narrating from 
    ‘Abd-Allaah ibn Dinar from Ibn ‘Umar: It is wealth on which zakaah is not 
    paid. Al-Thawri and others narrated from ‘Ubayd-Allaah from Naafi’ that Ibn 
    ‘Umar said: That on which zakaah is paid is not kanz, even if it is buried 
    beneath seven earths, but that  which is not buried and on which zakaah is 
    not paid is kanz. This was narrated from Ibn ‘Abbaas, Jaabir, and Abu 
    Hurayrah in both mawqoof and marfoo’ reports. ‘Umar ibn al-Khattaab said 
    something similar: Any wealth on which zakaah is paid is not kanz, even if 
    it is buried in the earth. And any wealth on which zakaah is not paid is 
    kanz with which its owner will be branded (on the Day of Resurrection), even 
    if it is on the face of the earth. End quote. 

    Thus it is clear that the kind of wealth that is blameworthy 
    is that on which zakaah is not paid. As for that which is beneath the 
    threshold (nisaab), or which reaches the threshold and zakaah is paid on it, 
    it is not kanz. 

    Thus it is clear that Islam does not forbid storing up 
    wealth, rather it forbids not paying zakaah on it. 

    And Allaah knows best.