The article is devoted to the analysis of the current legal norms governing the accrual of interest on the balance on the bank current accounts most in demand recently among individuals, namely the so-called “savings”/”savings” accounts of an individual, and the possibility of a bank changing the amount of accrued interest on the account balance, including by posting information on the establishment of a different amount of interest accrued by the bank on the account balance on the bank’s website on the Internet by analogy with the newly established tariffs and commissions. The necessity and possibility of obtaining the client’s consent by the bank to change the interest accrued on the account balance, as well as the form of such consent, the legal essence of the accrued interest, are analyzed. The analysis of the norms of legislation and practice made it possible to identify the problem that arises when working with the so-called “accumulative” account and come to the conclusion that it is necessary to improve the norms of current legislation.