IPMT

What it does

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

IPMT(rate,per,nper,pv,[fv],[type]) returns the interest part of a constant annuity payment in one chosen period. The period comes before the total count and starts at one. Future value and timing default to zero; type one means payment at the beginning.

Use a rate per payment period. A positive loan principal normally produces negative interest payments under Excel’s cash-flow sign convention.

Try it

=IPMT(0.25,2,2,1000) is about -138.8888889. On this two-payment loan, the interest in the second period is charged on the balance remaining after the first payment. =IPMT(0.25,1,2,1000,0,1) returns zero because a beginning payment at the initial instant has no elapsed-period interest.

Quirks

The documented period range is one through nper. The current helper returns #NUM! outside that range and distinguishes exactly zero rate from a tiny nonzero rate. Type is truncated by the wrapper before its zero/nonzero timing choice.

The newer source checks a valid beginning first period before its PMT rate guard, so it can return zero even at a rate PMT itself rejects. PPMT calls PMT first and can therefore have a different error path on that same otherwise invalid annuity.

Mathematically interest plus principal is the payment. Recorded Excel results can differ in their last bits from either subtraction identity: the notes retain a twelve-period example. Money amounts are not automatically rounded to cents by these functions.

How to implement

Use D and R for ordinary binary64 storage and a stored 64-bit-significand operation. The current route keeps argument validation, timing boundaries and period arithmetic separate.

1. Validate finite numeric arguments and require 1<=per<=nper. For beginning timing at per=1, return zero before PMT’s rate-domain and reciprocal-pole checks. At exactly zero rate, other valid periods also return zero.
2. For remaining calls reject a nonpositive growth base and obtain PMT under its own guards. A tiny nonzero rate retains the computation; do not use an epsilon band.
3. For end timing, fv=0 and a valid rate in the series range, obtain L and the total-period corrected exponential difference em_n from the PMT recipe. Store q=R(pv/em_n); do not recover q by dividing PMT’s already rounded answer by r.
4. Store m=D(D(nper-per)+1), then t=-D(m*L). Obtain the corrected difference em_m by the same spilled Kahan rule used for PMT.
5. Return -R(R(q*em_m)*r). Principal instead uses the separately stored EXP(t) result; 1+em_m is not a substitute for that exponential.

Worked second period of a two-period loan at r=0.25, pv=1000: the stated reconstruction has L 0.22314355131420974, total em_n -0.36000000000000004 and q -2777.7777777777774. One period remains, with em_m -0.19999999999999998; the stored products give interest -138.88888888888886. This trace evaluates the reconstruction, rather than adding an Excel capture.

For nonzero fv, the current end helper still forms v_n=D(1+em_n), N=D(pv+D(fv*v_n)) and q=R(N/em_n). Its interest expression is -R(R(R(q*em_m)-R(fv*EXP(t)))*r). This helper does not yet use the later nonzero-fv fold recovered for PMT itself. The note retains only 18 of 27 matching nonzero-fv interest controls; that numerator remains open here.

The helper declines rates outside its series range, opposite nonzero balances and zero/nonfinite em and nonfinite quotients. Beginning timing and other declined cases retain a separate backward-balance candidate with internal log1p/exponential leaves. They are not established by the zero-fv end-timing recipe. The source, first-period guard and unresolved fallback scope supersede the older page’s blanket recurrence description. The interactive calculator remains pinned separately.

Rust code

7 ipmt_fn "IPMT" (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::ipmt(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

PPMT returns principal and PMT the full payment. CUMIPMT totals interest over a period interval. ISPMT uses a different level-principal model and a different period convention.

Named variants

No named variants are recorded yet.