In the domestic economic cycle framework, savings and consumption play a crucial role as the driving forces propelling economic growth. As China experiences a deepening population aging process, within the context of overlapping generations where intergenerational income redistribution occurs, the intergenerational redistribution of the labor force is bound to increase. Nevertheless, a question arises: will savings decline? This is a specific and thought-provoking issue that merits in-depth exploration. Adhering to the principle of balanced redistribution across the life cycle, this paper establishes a mathematical model for the evaluation of population aging, income redistribution, and variations in the savings rate. It undertakes a comprehensive study on the changing trends of population aging, income redistribution, and the changes in savings structure, with the aim of delving into the driving forces behind economic growth under the circumstances of population aging. The research findings are presented as follows: (1) In the face of population aging and the growth in intergenerational redistribution, the savings rate does not necessarily experience a downward trend. On the contrary, savings targeted at mitigating the pension risks faced by the elderly witness an increase. By 2035, social pension savings are projected to rise by 11.87%. (2) As intergenerational redistribution expands, the consumption level of the elderly also ascends. By 2035, social elderly consumption is expected to increase by 13.13%. (3) In both the short and long term within China, the investment and consumption derived from pension savings constitute significant driving forces for economic growth. By 2035, their contribution to economic growth is anticipated to reach 0.55 percentage points. The research outcomes hold valuable reference significance for the implementation of strategies to actively respond to population aging.