As Secretary-General Annan prepares to leave his post at the United Nations, a mystery is surfacing surrounding his apartment on Roosevelt Island, subsidized by New York taxpayers, which is still in use by the family of his brother, Kobina Annan. The apartment was where Mr. Annan and his wife lived before 1997, when he became secretary-general. The Roosevelt Island home is part of an estate of low-rent state-regulated housing. For years, the Annans saved considerable sums by occupying an apartment meant to help financially strapped low- to moderate-income New York families. One question Mr. Annan has never addressed is why...