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Pension systems have been expecting projected deficits and governments have been under pressure to increase the statutory retirement age. Fully funded pension system pillars have significant limitations, the recent attempts to adapt social insurance systems have not provided plausible results and empirically have not had strong political support to be fully implemented. Therefore, we created an incentive-based pension system extension that enables a gradual transition to a merit-based pay-as-you-go system. We present a mathematical model based on virtual accumulation of resources that works with full working, relaxed and retired phases, based on the individual decision when to enter them. We present calculations based on the parameters that are valid in the Czech Republic, but the model is designed as a general one, therefore the model variables can be adjusted according to parameters in any country withpublic pension system. Then we discuss the implications and possibilities related to the model, also in the context of changes that we see in the labour market, behavioural patterns of the older generation and the socioeconomic development in the 21st century.