At retirement (30 years from today) you plan to shift your retirement account ($

Question

At retirement (30 years from today) you plan to shift your retirement account ($2 million balance) into a low risk investment earning 6% per year, compounded quarterly. You will then make 40 equal, semi-annual withdrawals from this account - the first withdrawal will occur 6 months into retirement (time 30 + 1/2), the last withdrawal will occur at time 50. After the last withdrawal (at time 50), the account will have a balance of $0. What equal dollar amount can be withdrawn every 6 months (i.e. semi-annually)?

Explanation / Answer

Pmt = Ar / (1-(1+r)-t)

The amount you deposit is A, the interest rate per period is r, the number of periods is t, and Pmt is the payment per period.

Effective interest rate with quarterly compounding:
=> (1 + i/n)n-1 = [(1)+(0.06/4)]4-1 = 0.06136

[($2,000,000) x (6.136%/2)] / [(1-(1+6.136%/2)-40)] = $87,480.92

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