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.
(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
Value of 500000 after 10 years or 40 quarters @3% per quarter =500000*(1.03^40) 1631018.90 On 10th Year Lee withdraws 150000 . So he is left with=1631018.90-150000 1481018.90 The value of the balance amount after another 12 years or 48 quarters @3% per quarter=1481018.9*(1.03^48) 6119943.13 (a) So the accumulated amount will not reach $8m (b)Short fall=8000000-6119943.13 1880056.87 Compound Value of an annuity=FV=A*[ (1+r)^n - 1)]/r Where A=Amount deposited every quarters, r=quaterly interest=3%,n=period=22*4=88 quarters So , A*(1.03^88-1)/0.03=1880056.87 or 415.985A=1880056.87 or A=1880056.87/415.985 4519.530 © PV of 20 milllion with 3% interest per quarter in 25 years or 100 quarters=20/(1.03^100) 1.041 So the amount Lee can withdraw as retirement benefit=(8-1.04)m 6.96 Present Value of an annuity=PV= A*[ (1+r)^n -1]/[(1+r)^n * r] where A=Amount received every quarters, r=quaterly interest=3%,n=period=25*4=100 quarters A*(1.03^100-1)/((1.03^100)*(0.03))=6960000 or 31.599 A=6960000 or A=6960000/31.599 220260.135
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