When you inherit an investment or bank account, you do not pay tax on the value of the account that you inherited. Assuming you inherit a taxable account (e.g., a non-retirement account), you will pay tax on the income you receive from the asset (i.e., dividend income, interest income) once you’ve inherited it, but you will not pay tax on the value of the account you inherit.
If you should later sell the asset (e.g., a stock in the investment account), you will realize either a capital gain or loss on the sale based on the difference between the cost basis and the sale price. For an inherited asset, the cost basis is the value of the asset on the date of death.
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