We analyze an investment strategy for an investor with a savings plan for retirement consisting on constraining the terminal wealth accumulated after the savings period by setting an upper and lower bound. We carry out a simulation of the terminal wealth after a savings period of thirty years by using daily, monthly, weekly and yearly updates. We calculate the percentiles of the final wealth and the corresponding lifetime annuity that the pension saver will receive during the consumption period. We observe how that the simulated values converge to the theoretical values of the percentiles when the frequency of update increases. Finally, in the numerical example the effect of inflaction is also considered.