2007 Essay Paper, Q1 (required return calculation)

So this question is pretty simple but why does the difference of the two methods below yield different results?

Q states: The guy wants is retired and will live for 35 years, he wants to preserve $3M and currently has $4.2M… He also spends $200K pretax a year (starting immediately with a withdraw) and inflation is 2.5%.

Now just plug and chug… the answer prescribed is Method #1, but why doesnn’t method#2 come up with the same answer?

Method #1 (using end mode): N=35, pv = -4 million, pmt = 205,000, fv = 3 million, compute i/y = 4.84% Here, they basically subtracted 200k immediately from the asset base, and adjusted for inflation for next year (200k x 1.025 = 205K)

Method #2 (using beg mode): N=35, pv = -4.2 million, pmt = 200,000, fv = 3 million, compute i/y = 4.64%

Because you do not earn return on the 200k you withdraw immediately. Aside from that, the PMT is not adjusted for inflation. This problem kind of confuses me because it does assume 205k is inflated only once, let alone the wording in general.

Well, the 2nd part I get… the reason they only inflate 205k once is because all numbers are real numbers at that point… PV is real, FV is real, etc.