1. Lee plans to retire in 22 years with a nest egg of $8M. He has already saved
ID: 2727954 • Letter: 1
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.
(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?
Explanation / Answer
(a) Future Value=A*(1+r)^n , where A=500000 , r=12/4=3% per quarter, n=10*4=40 quarters Future Value=500000*(1+0.03)^(40) 1631019 At 10th year he withdraws 150000 and so the balance at the end of 10th year will be=1631019-150000 1481019 In the next 12 years , this amount will grow to=1481019*(1+0.03)^(12*4) 6119944 No , the investment balance after 22 years will fall short of $8m (b) Short fall=8000000-6119944 1880056 He deposits quaterly amount for (22*4=88 quarters) to make up this short fall. Let the amount be A Compound Value of an annuity=FV=A*[ (1+r)^n - 1)]/r So, 1880056=A*(1.03^88-1)/0.03 or 1880056=415.98 or A=1880056/415.98 4519.58 So he has to deposit additional 4519.58 every quarter for 22 years to reach his goal of $8m. © Current deposit - PV of balance needed after 25years=8-(20/1.12^25) in million 6.82 So he can withdraw 6820000 for 25 years as annuity. The annuity factor of PV for (n=25 and r=12%)=7.33 So annual withdrawal=6820000/7.33 930422.9
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.