CUMPRINC follows PPMT on one loan and not in general; its own route is open

FN-CUMPRINC-001: CUMPRINC follows PPMT on one loan and not in general; its own route is open

Detail for matching Excel's bits · measured · recorded 2026-11-04

On the 30-year loan, CUMPRINC(0.05/12,360,200000,1,12,0) equals the left-to-right binary64 sum of Excel's own twelve PPMT answers, to the last bit, and CUMIPMT over the same periods equals 12*PMT - CUMPRINC, computed from Excel's own answers, to the last bit. That does not generalise: over recorded type 0 calls for a single period, CUMPRINC equals PPMT on 56 of 135 rows and differs on 79, with PPMT computed by the route in FN-IPMT-001.

Basis: One loan block of the catalogue capture, recomputed from the recorded answers by binary64 arithmetic, and 135 recorded single-period CUMPRINC rows compared with PPMT's route.

Inferred: That the 79 single-period differences are CUMPRINC's own and not PPMT's rests on the PPMT route, which matches every fv 0, type 0 row tested. That CUMIPMT remains count*PMT less CUMPRINC beyond this block is inferred.

Open: CUMPRINC's per-period route. Recurrences, closed balances, count*PMT less interest and binary64 variants all stay below PPMT's 56 of 135. Recorded rows now match CUMPRINC 185 of 586 and CUMIPMT 12 of 38.