PPMT is not PMT minus IPMT, and sits further from the exact value than PMT

FN-PPMT-001: PPMT is not PMT minus IPMT, and sits further from the exact value than PMT

Excel differs from the mathematical answer · measured · recorded 2026-11-04

On the 30-year loan PPMT(0.05/12,k,360,200000), for k from 1 to 12 every PPMT answer is 3 to 5 units above the correctly rounded principal payment, while PMT is 1 unit away. Excel's own answers do not satisfy the identity: in binary64, PMT - IPMT equals PPMT in 2 of the 12 periods and PMT - PPMT equals IPMT in 7. So reproducing PPMT from PMT and IPMT misses the last bits. FN-IPMT-001 gives the route Excel takes instead.

Correct value: mpmath at 800 bits with rate the binary64 0x3f71111111111111 that 0.05/12 evaluates to; correctly rounded.

Basis: Twelve recorded periods of one loan, read from the catalogue capture, compared with exact values and with Excel's own PMT and IPMT by binary64 subtraction, recomputed for this note.