PPMT

What it does

PPMT(rate, per, nper, pv, [fv], [type])

PPMT(rate,per,nper,pv,[fv],[type]) returns the principal part of one payment in a fixed-rate, equal-payment annuity. Period per starts at one and precedes nper in the argument list. Omitted fv and type are zero; type one pays at the beginning.

Try it

=PPMT(0.25,2,2,1000) is about -555.5555556, the final principal repayment on a two-period loan. The first principal repayment is about -444.4444444, so the mathematical pair repays the original thousand.

=PPMT(0,2,4,1000) returns -250; at zero rate all four equal payments are principal.

Quirks

Use a periodic rate and a matching period count. Positive principal and negative repayments describe a loan. Per must lie between one and nper; the current helper checks it through IPMT after obtaining PMT.

PPMT’s current first operation is a PMT call. It can therefore return a PMT domain error where IPMT’s beginning-first-period guard returns zero. At a valid beginning first period the whole payment is principal.

The mathematical identity PPMT=PMT-IPMT does not reproduce all recorded Excel bits. FN-PPMT-001 retains twelve loan periods where only two such binary64 subtractions equal the recorded principal. Summing principal over a schedule and reproducing CUMPRINC are separate numerical tasks.

How to implement

For the measured zero-fv, end-timing route, reuse L, total-period em_n and the stored q from the IPMT recipe. Let R denote its stored arithmetic operation.

1. Obtain PMT and perform the IPMT guard path, including period validation. Exactly zero rate uses the linear principal result.
2. For the eligible nonzero-rate helper, form the binary64 remaining count m=(nper-per)+1 and argument t=-(m*L), with each named operation stored.
3. Obtain the stored public exponential u=EXP(t). Do not replace it by 1+em_m: the note’s 74 principal controls distinguish those values.
4. At fv=0 return R(R(q*u)*r). With a nonzero fv, the current candidate is R(R(R(q-fv)*u)*r), but q’s nonzero-fv numerator retains the limitation described on IPMT.

For the second-period example, the reconstruction has q -2777.7777777777774, u 0.8 and principal -555.5555555555555. Its PMT is -694.4444444444443 and interest -138.88888888888886; ordinary binary64 subtraction of those two produces -555.5555555555554 instead. These are worked reconstruction values, not a new Excel run.

The source retains 138 of 138 zero-fv principal controls and 25 of 27 nonzero-fv controls for its end route. Beginning timing and helper-declined cases use a separate backward-discount candidate, rather than simply subtracting interest. Its current form discounts payment-carried_future_interest over the periods remaining, with a beginning-timing adjustment to that carried interest.

The logarithm’s exceptions, nonzero-fv numerator, beginning-timing body and other recorded residuals remain open. Reusing PMT’s newer balance fold without separately validating these period helpers would transfer a result outside its established scope. The separately pinned calculator can predate the cited source changes.

Rust code

8 ppmt_fn "PPMT" (4, 6) [V "rate", V "per", V "nper", V "pv", V "fv", V "type"] |s, a, sv| {
    let t = timing(s, a, 5)?;
    tv_out(s, tv::ppmt(num(s, a, 0)?, num(s, a, 1)?, num(s, a, 2)?, num(s, a, 3)?, opt(s, a, 4, 0.0)?, t))
}

No implementation has been published with a Handbook test suite for this function.

Version differences

The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.

The record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.

Recorded environments and comparison details.

Alternatives

IPMT returns interest and PMT the entire payment. CUMPRINC totals principal over an interval, with a separately recorded route; ISPMT belongs to a level-principal schedule.

Named variants

No named variants are recorded yet.