Question

You have an account with $5,500,000 that has an expected return of 8.5% per year. Exactly one year after you create this account you will make your first withdraw and continue for 25 years when your account is $0. Your withdraw grows by 2% every year to adjust for inflation. What is your first withdraw amount?

Answer 1

Present value of account is $5500,000

You will withdrawal 25 yearly amounts from this account that will increase 2% on each subsequent withdrawal.

calculating the First withdrawal using Present value of Growing annuity formula:-

Present Value = C*{1-[(1+g)^(n)*(1+r)^(-n)]}/(r-g)

Where, C= First Withdrawal

r = Periodic Interest rate = 8.5%

g = Inflation rate = 2%

n= no of periods = 25

Present Value = $5,500,000

5,500,000 = C*{1- [(1+0.02)^(25)*(1+0.085)^(-25)]}/(0.085-0.02)

5,500,000 = C*{1- [1.64060599446*0.13009378379]}/(0.065)

357,500 = C*[1- 0.21343264152]

357,500 = C*0.78656735848

C = $454,506.53

So, your first withdraw amount is $454,506.53

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