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Is it insecure to provide a hash of an AES password?

I have made some software that encrypts and decrypts files using AES. I was wondering if it is safe to write a hash of the password to the file so that the program can check if a password is correct. The reason I am worried about this is because, without the hash, for a file that takes ten seconds to decrypt, one million attempts at cracking the encryption take ~115 days. Whereas, with the hash, regardless of the size of the file, one million attempts will take roughly 5 days if one attempt takes 0.5 seconds (much more than reality). This is a huge difference, hence my concern: Is it less secure to write the hash of an encrypted file's password to the file?