Lee plans to retire in 22 years with a nest egg of $5M. He has already saved up $300,000 in an investment account that generates an annual rate of return of 12.6%, compounded daily. Assume 360-day year and 30-day month in your analysis!

 (a) Numerically show whether Lee's investment account balance will reach $5M in 22 years, based on the information provided above.

(b) The correct answer for part (a) indicates that Lee's investment account will fall short of his retirement goal of $5M in 22 years. Thus, he continues his pursuit by making additional fixed contributions at the beginning of each quarter to the same investment account until he retires 22 years later. Calculate the amount of his quarterly contribution needed for achieving his goal. 

 (c) Lee now retires with $5M that is transferred to a retirement account offering an annual return of 6%, compounded monthly. He withdraws monthly from the retirement account to cover his living expenses that grow at a monthly inflation rate of 0.3%. Lee takes out his first withdrawal of $21,500 at the end of the month. Calculate the amount of Lee's inheritance upon his death after enjoying 24 years of retirement.