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Weapons and ammunition are stored in an armory, magazine, silo, arsenal or at a weapons or ammo dump. In a home they should be stored in a secure safe or chamber/trigger locked with ammunition locked up separately.
Weapons are kept in Armouries. Ammunition is kept in a magazine. They should not, never ever, be stored together.
Arsenal or armory.
Arsenal
armoury
a weapon cache
An armoury is a place where weapons are kept (stored).
Explosive room
Armoury, magazine, or silo. Probably others also.
Often times a storage place for weapons and ammunition is called an arsenal. In US history one of the most famous such arsenals was located at Harper's Ferry in Virginia.
Armoury, magazine, or silo. Probably others also.
All ammunition, if kept stored in a cool dry place, will be good for multiple decades.