thisisbrianly

you answer ($8497) is correct if you only wish to receive a nominal payout of $42000 per year.
your friend wishes to calculate in real terms (by factoring inflation) which would make more sense if you wish to receive future payouts equivalent to the purchasing power of todays $3500. however your friend's calculation is incorrect.
1. to compute in real terms use the real discount rate which is 1.96% in your case. use the equation (1+nominal rate) = (1+real rate) x (1+inflation) and 4% nominal rate, 2% inflation to get the 1.96%. in general, real rate is approx = nominal rate minus inflation.
2. BGN mode, N=20, I/Y=1.96%, PMT=42000 to get PV = -702883 which is the present value (at t=34) in real terms of your 20 annual post retirement payouts .
3. convert the 702883 real amount to a nominal amount using the inflation factor 1.96 = 1.02^34. that amount is 1378126. this amount is the PV (at t=34) of your future nominal payouts.
4. now that you have the nominal amount, use the nominal rate of 4% with N=34, I/Y=4%, FV=1378126, to get PMT=-19727. hence you would need to set aside 19727 each year for 34 years.
5. if you wish to stick with nominal amounts / discount rates (easier to understand but cumbersome with a calculator, easier with a spreadsheet) you may wish to set up your calculation in nominal terms. to receive the real equivalent of $42,000 per year in future you would want to receive 82348 (just as you have computed) in year 34, 83995 (82348 x 1.02) in year 35 and so on. then solve for the required payments using the nominal 4% discount rate. you should get the same answer.