FWIW... looking at single life anniuties, between ages 44 and 45, comparing your actual calculations with interpolation to integer months, the largest difference (age 44 and 6 months) was less than 0.07% with mortality, and less than 0.03% without mortality. Choice of different interest rates (look-back months) produces much larger differences. By using our "manual" calculations for J&S annuities, we had intended to interpolate integer ages, assuming that the small differences for single life annuities will be essentially true for J&S annuities. So, yes, if your program does J&S annuities for integer ages, it will be very useful. Will hopefully be looking for your updated program next week> Thanks again...