1)Lee plans to retire in 22 years with a nest egg of $8M. He has already saved $
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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.
Numerically show that whether Lee’s investment account balance will reach $8M in 22 years, based on the information provided above.
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?
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?
2)Maryanne, a baby boomer who turns 50 today, begins to save for retirement with $200,000 that she just receives from a trust fund. She immediately invests this $200,000 in a stock fund. In addition, she plans to contribute $10,000, $15,000, and $20,000, respectively, at the end of the next 3 years to the same stock fund. The stock fund generates a nominal rate of return of 10%, compounded annually.
What will be the value of her stock fund when she retires at the age of 67?
Right after her retirement, she transfers her nest egg into a conservative investment that compounds monthly. If Maryanne wants to withdraw a fixed monthly payment of $7,000 from this investment indefinitely, what should be the annual rate of return of this conservative investment?
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=12.55/4=3.138% 1881159=A*(1.03138^88-1)/0.03138 A =$4167.33 So Quarterly deposit required =$4,167.33 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 +10000000/1.1255^25=8000000 A*7.5534 +520430.23=8000000 A=990225.56 So Maximum Annual withdrawal is $990,225.56 2 Year 0 Year 1 Year 2 Year 3 Investments 200,000 10,000 15,000 20,000 Years of compounding 17 16 15 14 Compounding Factor @10% 5.0545 4.5950 4.1772 3.7975 Maturity Value 1,010,894 45,950 62,659 75,950 Total Maturity value at the age of 67 1,195,452 Assume the monthly interest rate =k so , k*1195452=7000 k=0.5856% So Annual ineterest rate is 7.03% compounded monthly
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