Hypothetical question on investment

banebt

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Hi all
I am ashamed to say that i forgot some of the concepts in Level 3 and now that i need them for my work i cant really get find a solution
The problem:
Initial investment 1 mil
retirement after 10 years
Lump sum income on day of retirement 200k
Last year expenses 60k
life after retirement 30 years
Inflation 2%
Disregard taxes
What is the required return if at the end of 30 years i dont want to have anything. So start using my capital after 10 years and deplate it 100% at the end of life.
I worked out the living expenses at first year of retirement are 60 x 1.02^10 = 73 140
I can solve it if i assume that i want to keep real value of my initial investment but i cannot figure out how to do it if i want to spend all of my wealth at the end of my life. The issue is that my expenses 73 140 will grow at inflation
I can work out with help of excel but i want to find the formula behind it
Thank you very much folks
Regards,
 
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