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%**