In this paper, we develop and numerically solve a model of idiosyncratic labour income and idiosyncratic interest rates to predict the evolution of a wealth distribution over time. Stochastic labour income follows a deterministic growth trend and it fluctuates between a wage and unemployment benefits. Stochastic interest rates are drawn initially (ex-ante heterogeneity), fluctuate between two values (ex-post heterogeneity) and can differ in their arrival rates (financial types). A low interest rate implies a stationary long-run wealth distribution, a high interest rate implies non-stationary wealth distributions. Our baseline model matches the evolution of the wealth distribution of the NLSY 79 cohort from 1986 to 2008 very well. When we start in 1986 and target 2008, we obtain a fit of 96.1%: The fit for non-targeted years is 77.0% on average. When targeting the evolution of wealth, the fit is 88.9%. With a more flexible interest rate distribution, the fit can even be increased to 96.7%. Comparing calibrated mean returns with data shows that the flexible interest rate distribution has empirically not convincing "superstar states". In the baseline model, mean returns are empirically convincing. Surprisingly, the standard deviation of model returns is an order of magnitude lower than the empirical standard deviation.