The credit will not be greater than the US tax on the income. If the other country has a higher tax rate, you would not get the full credit. If you want to see all the intricacies of the form, see Figuring the Credit in Instructions for Form 1116. Notice your foreign income compared to your world income is part of the calculation.
Usually interest earned while a resident here is taxable to the US but each treaty is different. See United States Income Tax Treaties to see if you can exclude your income.
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