Sandy plans to retire in 22 years with a nest egg of $8M. She has already saved $500,000 in an investment account that generates a nominal rate of return of 12%, compounded quarterly. However, she needs to withdraw $150,000 from this account in 10 years to finance her daughter’s college education.
(a) Numerically show that whether Sandy’s investment account balance will reach $8M in 22 years, based on the information provided above.
(b) The correct answer for part (a) indicates that Sandy’s investment account will fall short of her retirement goal of $8M in 22 years. Thus, she continues her pursuit by making additional fixed contributions at the end of every quarter to the same investment account until she retires 22 years later. How big should be her quarterly contribution in order to achieve her goal?
(c) Assume now that Sandy retires and has $8M in her investment account. If she wants to leave $10M to each of her two children upon her death after enjoying 25 years of retirement. What is the maximum annual withdrawal from the investment account Sandy can make at the beginning of every year during her retirement?
PS: The answer to the questions was provided by the instructor, i need a detailed solution of how to arrive at the answers provided.