Lee plans to retire in 22 years with a nest egg of $8M. He has already saved $50

Question

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.

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?

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?

every year during his retirement?

Explanation / Answer

Details   Lees Current return =12% compounded quarterly            1 Effective annual Rate =(1+0.12/4)^4-1= 12.55% So EAR is 12.55% Investment amt =$500,000 Maturity amount after 10 years =500000*1.1255^10 =             1,630,891 Less Withdrawal as per plan =              (150,000) Amount remaining after the withdarawal=             1,480,891 Maturity Value of 1,480,891 after another 12 years@12.55%=             6,118,841 So Lee will fall short of $8M target   Shortfall is $8000000-6118841=             1,881,159 Assume lee deposits $ A each qtr for 22 years to make up for this shortfall FV of Annuity =A*[(1+k)^n-1]/k N =88 qrtrs k=(1+0.1255)^(1/4)-1= 2.9998% 1881159=A*(1.029998^88-1)/0.029998 A =$4522.71 So Quarterly deposit required =$4,522.71 Assume Lee can withdraw max $A per year   PV of Annuity =A*[1.1255^25-1]/0.1255(1.1255)^25 As per condition : A*[1.1255^25-1]/0.1255(1.1255)^25 +20000000/1.1255^25=8000000 A*7.5534 +1040860=8000000 A=921325 So Maximum Annual withdrawal is $921,325

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