Insurance companies employ legions of actuaries. They make really good money for mostly just plugging data into a formula. Insurance companies have created an industry out of making sure they make a good profit.I don't think you need to be an actuary to do the calculation.
So the math seems manageable. The tricky part is deciding which table to use. Should I use Total US Population? Or Total Male Population? or White Male Population? Should I adjust for the fact that I'm healthy today, and the mortality table includes people who are terminally ill today? Should I adjust for the expected improvement in mortality rates in the future? That seems more challenging to me.
As has been stated many times before, the IRR is determined by how long someone continues to receive payments. Assuming you will live past your mortality table lifespan makes a SPIA look really good. It does not change the fact that among all the people purchasing the annuity half will die before that date. So ask yourself, do you feel lucky? If the answer is yes, buy the SPIA and stop repeating the same absurd thread over and over.