1. Lee plans to retire in 22 years with a nest egg of $8M. He has already saved
ID: 2728271 • 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. <Answer should be $6.12M>
(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? <Answer should be $4,519.39>
(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? <Answer should be $818,587.57>
Explanation / Answer
B) Future value @ 12% int rate compounded quarterly is $ 6.12 M against $ 8 M
Diffrence come to $ 1.88 $
So Amt to be contributed in such way that amt come to $ 1.88 million
So amt investment in quater = $ 1.88 M/ (1+ 1.1255)22 Year
= $ 4519
Year Amt in investment account withdrawal Amt remain in investment account after his withdrawal Bal Int rate @12% compounded anually 1 500000 0 500,000 563000 1.126 2 563000 0 563,000 633938 1.126 3 633938 0 633,938 713814 1.126 4 713814 0 713,814 803755 1.126 5 803755 0 803,755 905028 1.126 6 905028 0 905,028 1019061 1.126 7 1019061 15000 1,004,061 1130573 1.126 8 1130573 15000 1,115,573 1256135 1.126 9 1256135 15000 1,241,135 1397518 1.126 10 1397518 15000 1,382,518 1556716 1.126 11 1556716 15000 1,541,716 1735972 1.126 12 1735972 15000 1,720,972 1937814 1.126 13 1937814 15000 1,922,814 2165089 1.126 14 2165089 15000 2,150,089 2421000 1.126 15 2421000 15000 2,406,000 2709156 1.126 16 2709156 15000 2,694,156 3033620 1.126 17 3033620 15000 3,018,620 3398966 1.126 18 3398966 0 3,398,966 3827236 1.126 19 3827236 0 3,827,236 4309467 1.126 20 4309467 0 4,309,467 4852460 1.126 21 4852460 0 4,852,460 5463870 1.126 22 5463870 0 5,463,870 6152318 1.126Related Questions
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