Please show details how to resolve the following: Question $1$

Assume that our client, GeekTech Inc. is a publicly traded technology company. GeekTech Inc. faces a marginal tax rate of $40\%$ and applies a plow$-$back of $50\%$ of Net Income into Retained Earnings.

First, you are to create the necessary Balance Sheets and Income Statement and then calculate the annual Cash Flow from Assets $($aka: CFFA or Free Cash Flows $($FCF$))$ for GeekTech Inc. A constraint here, however, is that your last CFFA $($aka: CFFA$\_0)$ must range between $$100,000,000$ and $$125,000,000$ annually.

Second, after calculating GeekTech Inc.$\text{'}$s last CFFA, you are to assume that this corporation is a constant$-$growth perpetuity and estimate its present value $($aka: intrinsic value, market value$).$

Assume the market determined risk adjusted required rate of return $($aka: the appropriate discount rate, WACC$)$ for GeekTech Inc. is $8\mathrm{.}50\%$ and the annual growth rate in GeekTech Inc's CFFA is $4\mathrm{.}00\%.$

Question $2$:

GeekTech Inc. is confused about their understanding of the convergence of a finite series of cash flows $($aka: annuity$)$ to the value of a perpetuity $($aka: no growth perpetuity$).$ Specifically, they are confused about the fact that lower rates converge faster than higher rates.

First, provide an example of how lower rates converge faster than higher rates. Second, what are the implications from lower rates converging faster to the present value of a perpetuity than higher rates.