An investment is expected to generate monthly cash flows forever, with the first cash flow coming exactly $1$ month from today and each subsequent cash flow coming exactly one month after the previous cash flow. The amount of the first cash flow is expected to be $$3.$ Each subsequent cash flow is expected to be $1+$g times the amount of the previous cash flow. The discount rate applicable to this investment is $12\%$ per year compounded monthly. The value of this investment today is $$400.$ What is the growth rate, g$,$ of the cash flows generated by this investment? Round all intermediate calculations to $6$ decimal points. Your final answer should be within $0\mathrm{.}05\%$ of the correct answer choice.