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No, there is no rule that loans or bonds at higher interest rates take priority over those at lower interest rates. In bankruptcy, secured debts take priority over unsecured debts. For corporations or governments in bankruptcy, the seniority of the debt also determines the order in which the debts are paid. In both cases, the interest rate is not a determining factor.

If you are asking about paying off consumer credit, it is true that it generally works out that paying off the higher interest rate loans (e.g., credit cards) first is the best strategy, simply because the interest on those can make it virtually impossible to make any headway on paying off the total personal debt. Again, that's not a rule, but the arithmetic usually works out that way.

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