We develop and analyze an intertemporal cost of living index (ICOLI), also referred to as lifetime cost of living or cost of life index. The ICOLI is a geometric weighted average of effective prices, derived from constrained consumer utility maximization. Effective prices are both, money valued marginal utilities of the final unit consumed, and present values of prices for future consumption. Using the concept of duration, we derive analytical elasticities of the ICOLI with respect to consumer prices and interest rates and show their impact on lifetime welfare of consumers. We also provide empirical evidence for Germany, compute an ex post time series of the ICOLI, and gauge the welfare effects of low interest rate scenarios. We find that the financial repression policy of the ECB since 2010 contributed to substantial losses in the purchasing power of money and led to lasting welfare losses for consumers in Germany, in particular for the cohorts of young consumers. The ICOLI complements conventional price and inflation statistics and could serve as a valuable information tool for monetary policy.