The two best predictors of children's educational achievement available from birth are parents' socioeconomic status (SES) and, recently, children's inherited DNA differences that can be aggregated in genome-wide polygenic scores (GPS). Here, we chart for the first time the developmental interplay between these two predictors of educational achievement at ages 7, 11, 14 and 16 in a sample of almost 5,000 UK school children. We show that the prediction of educational achievement from both GPS and SES increases steadily throughout the school years. Using latent growth curve models, we find that GPS and SES not only predict educational achievement in the first grade but they also account for systematic changes in achievement across the school years. At the end of compulsory education at age 16, GPS and SES, respectively, predict 14% and 23% of the variance of educational achievement. Analyses of the extremes of GPS and SES highlight their influence and interplay: In children who have high GPS and come from high SES families, 77% go to university, whereas 21% of children with low GPS and from low SES backgrounds attend university. We find that the associations of GPS and SES with educational achievement are primarily additive, suggesting that their joint influence is particularly dramatic for children at the extreme ends of the distribution.