The double ageing of the population leads to income redistribution from future to present generations as net payments to social health insurance are negative at young age and positive at old age. Economists arguing in favour of flat health insurance premiums combined with ageing provisions often neglect the transition from the pay-as-you-go to funded system. Using a generational accounting approach we analyze a reform to funded premiums, taking into account the transition. Furthermore, we implement a tax-transfer scheme designed to protect low income persons facing higher payments in the premium scheme. Our calculations reveal that under the current pay-as-you-go system German social health insurance burdens future generations by almost 30 percent of GDP. Funding could reduce this burden to 5 percent of GDP but would involve higher payments up to 700 Euro p.a. for the present generations. A delay of the reform would increase the burden for future generations again and benefit baby boomers born before 1970. We conclude from a public-choice perspective that it will be difficult to implement even a delayed reform to a more funded health insurance system.