He or she shall, at the end of each month and as often as may be required, render a report to the Mayor and City Council showing, under oath, the condition of the various accounts of the treasury at the time of such reports and the balance of money in the treasury; he or she shall accompany such accounts with a statement of all receipts and disbursements, together with all warrants paid by him or her, which warrants with any and all vouchers held by him or her shall be filed with his or her accounts in the City Clerk’s office. He or she shall keep a record, in a book suitable for that purpose, of each and every warrant paid and from what fund paid. He or she shall also produce depository evidence that all city money is in a solvent and going bank in the name of the city. If the City Treasurer neglects or fails, for a period of ten days from the end of each and every month, to render his or her account, the City Council shall by resolution declare the office vacant, and the Mayor and City Council shall fill the vacancy by appointment.