DALLAS — Associates First Capital Corp. said Thursday that it has agreed to buy a majority interest in Unimat Life, the ninth-largest consumer finance company in Japan. Terms were not disclosed.

The deal carries out Associates First’s stated strategy of adding to its business in Japan even though the company itself is being bought. On Sept. 6, Citigroup Inc. announced that it had agreed to buy Associates First in a deal that is slated to close this year.

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