Articles in "Journal of Accountancy," have discussed the handling of discount or premium on bonds which are refunded in various issues published as of January 1946. The Committee on Accounting Procedure of American Institute of Accountants in its September 1939 issue of "Accounting Research Bulletin," was hesitant in expressing definite conclusions but, more important, neglected an enlightened approach by refusing to consider it opportune to discuss the theoretical soundness and practicability of adopting an alternative treatment of bonds which would recognize in some respects the nominal character of the terms "principal" and "interest." The mere existence of premium or discount, however, is complete evidence that face value is not the exact principal, and that face value or principal is nominal only. By considering reality much confusion can be avoided, and this is the author's approach. Where others avoid a positive position, the author proposes by mathematical analysis of the facts to indicate the only proper methods.