Why do we not add the inflation component in the PV, FV, PMT, N but do add the inflation component when doing the other method of: nominal = real + inflation
the answer has two parts
If you look historically at all questions where this method is used - the usual approach to applying this methodis highlighted in the question stem itself. Question stem usually would state what return requirement will meet this objective… have a X value in N years e.g. For this - your PV which is the current net investable assets - already includes inflation compnent. The X value FV also has inflation included (it is the value required after accounting for N years of Inflation). Your PMT is a end of year payment in terms of set up (so has inflation for this period included). Hence the I/Y includes Inflation already.
The other type of question - where you do Income, Expenses, etc. etc. and arrive at the return required for the “first year of retirement” in the stem - needs the add on inflation portion - because you need to maintain the purchasing power of the portfolio - hence the add-on inflation component.
thank you!