Corporate finance class question

Question 1

Lee plans to retire in 22 years with a nest egg of $8M. He has already saved $500,000 in an investment account that generates a nominal rate of return of 12%, compounded quarterly. However, he needs to withdraw $150,000 from this account in 10 years to finance his son’s college education.

(a) Numerically show that whether Lee’s investment account balance will reach $8M in 22 years, based on the information provided above. The Answer = $6.12M

(b) The correct answer for part (a) indicates that Lee’s investment account will fall short of his retirement goal of $8M in 22 years. Thus, he continues his pursuit by making additional fixed contributions at the end of every quarter to the same investment account until he retires 22 years later. How big should be his quarterly contribution in order to achieve his goal? The Answer=$4,522.18

(c) Assume now that Lee retires and has $8M in his investment account. If he wants to leave $10M to each of his two children upon his death after enjoying 25 years of retirement. What is the maximum annual withdrawal from the investment account Lee can make at the beginning of every year during his retirement?

The Answer =$818,587.57

PS:The answer to the questions was provided by the instructor, i need a detailed solution of how to arrive at the answers.

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