Which type of bond is non-marketable, issued at a discount, and has interest exempt from state and local taxation?

The correct choice is Series EE bonds because they possess specific features that align with the description provided. Series EE bonds are non-marketable, meaning they cannot be bought or sold on the open market; they are issued by the U.S. Department of the Treasury and can only be redeemed through the Treasury. These bonds are sold at a discount to their face value, which allows the government to offer them at a lower initial purchase price, providing an investment that appreciates to its face value over time.

Furthermore, the interest earned on Series EE bonds is exempt from state and local taxes, making them an attractive investment for individuals looking to avoid these taxes while still earning interest. This tax advantage is particularly significant for investors who may be in higher state and local tax brackets.

Other types of bonds, such as convertible bonds, subordinated debentures, and bonds with a claim on assets, have distinct characteristics that do not include the combination of being non-marketable, issued at a discount, and having tax-exempt interest. These other bond types involve elements like being traded in markets or having different structures concerning claims on assets or conversion features, which do not match the criteria specified in the question.