A method for preparing a compound of the following formula: wherein: • R 3 represents H or a linear or branched R 4 alkyl group, comprising from 1 to 6 carbon atoms, • R 1 represents: F, Cl, Br, CF 3, or a linear or branched alkyl group, comprising from 1 to 6 carbon atoms, said alkyl group being optionally substituted by a halogen atom; and • n is equal to 7, 8, 9, 10, 11, 12, 13, or 14, said preparing method comprising: - implementing the Wittig-Horner reaction by the reaction of a phosphonate of the following formula: wherein: - R 1 is as defined above, - R 2 represents a linear or branched alkyl group, comprising from 1 to 6 carbon atoms, and is preferably an ethyl or methyl group, said R 2 groups being able to form a ring with the oxygen atoms of the OR 2 groups and the phosphorus atom of the P=O group, and - R 4 represents a linear or branched alkyl group, comprising from 1 to 6 carbon atoms, and is preferably an ethyl group, on a lactol of the following formula: n being as defined above, in order to obtain a hydroxy-ester of the following formula: wherein n, R 1 and R 3 are as defined above, - and, optionally, when R 3 represents an R 4 group as defined above, a saponification reaction of the abovementioned hydroxy-ester of the formula, to obtain a hydroxy-acid of the following formula: wherein n and R 1 are as defined above. • R 3 represents H or a linear or branched R 4 alkyl group, comprising from 1 to 6 carbon atoms, • R 1 represents: F, Cl, Br, CF 3, or a linear or branched alkyl group, comprising from 1 to 6 carbon atoms, said alkyl group being optionally substituted by a halogen atom; and • n is equal to 7, 8, 9, 10, 11, 12, 13, or 14, said preparing method comprising: - implementing the Wittig-Horner reaction by the reaction of a phosphonate of the following formula: wherein: - R 1 is as defined above, - R 2 represents a linear or branched alkyl group, comprising from 1 to 6 carbon atoms, and is preferably an ethyl or methyl group, said R 2 groups being able to form a ring with the oxygen atoms of the OR 2 groups and the phosphorus atom of the P=O group, and - R 4 represents a linear or branched alkyl group, comprising from 1 to 6 carbon atoms, and is preferably an ethyl group, on a lactol of the following formula: n being as defined above, in order to obtain a hydroxy-ester of the following formula: wherein n, R 1 and R 3 are as defined above, - and, optionally, when R 3 represents an R 4 group as defined above, a saponification reaction of the abovementioned hydroxy-ester of the formula, to obtain a hydroxy-acid of the following formula: wherein n and R 1 are as defined above. - implementing the Wittig-Horner reaction by the reaction of a phosphonate of the following formula: wherein: - R 1 is as defined above, - R 2 represents a linear or branched alkyl group, comprising from 1 to 6 carbon atoms, and is preferably an ethyl or methyl group, said R 2 groups being able to form a ring with the oxygen atoms of the OR 2 groups and the phosphorus atom of the P=O group, and - R 4 represents a linear or branched alkyl group, comprising from 1 to 6 carbon atoms, and is preferably an ethyl group, on a lactol of the following formula: n being as defined above, in order to obtain a hydroxy-ester of the following formula: wherein n, R 1 and R 3 are as defined above, - R 1 is as defined above, - R 2 represents a linear or branched alkyl group, comprising from 1 to 6 carbon atoms, and is preferably an ethyl or methyl group, said R 2 groups being able to form a ring with the oxygen atoms of the OR 2 groups and the phosphorus atom of the P=O group, and - R 4 represents a linear or branched alkyl group, comprising from 1 to 6 carbon atoms, and is preferably an ethyl group, - and, optionally, when R 3 represents an R 4 group as defined above, a saponification reaction of the abovementioned hydroxy-ester of the formula, to obtain a hydroxy-acid of the following formula: