We develop a novel structural economic model of overlapping generations to study wealth accumulation and distribution under the shared socioeconomic pathways (SSPs). We consider skill-specific wages and intergenerational wealth transfers as determinants wealth. The model is calibrated to match the projections of human capital accumulation and economic growth of South Africa in the 21st century. We find that the wealth gap between the rich and the poor increases under the SSP3 and SSP4 scenarios which have lower human capital growth rates. Furthermore, rich households accumulate more wealth at a faster rate than poor households. In other scenarios, the median households with mixed skill background are those leading the wealth accumulation compared to rich households. As a result, the wealth gap grows slower and the wealth inequality measured by the Gini index decreases in SSP1, SSP2, and SSP5. Overall, our results highlight the important role of capital inheritance in the income distribution dynamics.