So, in the sense of “financial transactions” or “monetary documents”, the rules of the Russian language allow the use of two options: on the account and on the account.
For example, you can freely say and write: There are not enough funds in the phone account (or in the phone account), I prefer to keep the money in a bank account (or in a bank account), the bank has the privilege to use the available funds in the account (or in the account) at its own discretion.
If the word “count” is used as a noun for the verb “count”, then the following options will be correct: lose count and count (make a mistake when counting), there will be no count and will not count, will not count and without counting (“ a lot”).
If the noun “count” conveys the meaning “to be recognized, to be regarded as something”, then the variant with the stressed ending -y will be used: “Anna Pavlovna had a good reputation, her children seemed to love and obey her…” (G . Troepolsky).
The emphasis on the vowel “u” is also used to mean “to be in limited quantity”: “I know that every penny counts for you now” (Valentin Rasputin).
If in doubt when choosing the form of a word, experts advise consulting Mikhail Studiner’s “Dictionary of difficulties of the Russian language…”.
