It seems that modern course books still show table based calculations of the APVs of mthly life contingencies being done using lx tables which only have lx tabulated for integer values of x, leading, if m>1, to the calculation being approximated by either:

Calculating the APV of the mthly life contingency using the table, interpolating in the cases of the non integers within the calculation.

Or first calculating the APV of the corresponding (same x, n (if temporary) and v) yearly life annuity due using the table, and then applying the Euler-Mclaurin based “Woolhouse approximation formula” to this, thus obtaining the approximate APV of the corresponding (same x, m, n (if temporary) and v) mthly life annuity due, and finally, if needed, applying to this, the standard identity formula (making the APV of the mthly life contingency the subject of this formula) which connects the APV of the mthly life contingency to the APV of the corresponding (same x, m, n (if temporary) and v) mthly life annuity due.

Accurate table based calculations of the APVs of mthly life contingencies would certainly, of course, be achieved by doing these calculations using accurate lx tables which have lx tabulated for x in steps of 1/m, and, in fact, because the only practical values for m are m=1, 2, 3, 4, 6 or 12 and 1/1=12/12, ½=6/12, 1/3=4/12, ¼=3/12, 1/6=2/12 and 1/12=1/12, accurate table based calculations of the APVs of mthly life contingencies would be achieved by doing these calculations using accurate lx tables which have lx tabulated for x in steps of 1/12. Is it not possible to produce such lx tables, and if not, then why not?