We develop a continuous time framework for sequential goals-based investing, where the objective is to maximize expected weighted utility from goal fundedness. A stochastic factor process drives price dynamics, goal amounts, and cash infusion into the client's portfolio. Using a generalization of the mean-variance efficient frontier, we show that the computational complexity of the procedure to recover the optimal control can be significantly reduced by rewriting the HJB equation in terms of standard deviation and mean of minimum-variance portfolio returns, and covariance of such portfolio returns with the state process. Our analysis highlights the fundamental tradeoff between immediate goal consumption versus saving towards future goal liabilities. We find that it is optimal to fund an expiring goal up to the level where the marginal benefit of additional fundedness is exceeded by the marginal opportunity cost of subtracting wealth from future goals. An investor with all-or-nothing utility is more risk averse towards an approaching goal deadline if she is well funded, but also takes excessive risk if she is not on track with upcoming goals, compared to an investor who maximizes the weighted expected goal fundedness.