Prime and Saturn calculators

[Albert Chan]

(07-07-2024 08:24 PM)dm319 Wrote:  So I think you've deduced the HP-12c uses the NPV formula?

NPV=0 is in HP-12c manual, Appendix D, formulas used.

Quote:I can't prod the HP-12c platinum into getting a negative result, but the result does vary depending on what was input into i to begin with. Maybe they extended the stopping criteria as they had more performance to work with?

HP-12cp has internal 15 digits, whereas HP-12c has 13.
This may be a case of solving problem by throwing precisions to it.

(07-07-2024 01:37 PM)Albert Chan Wrote:  With good expm1/log1p, fuzziness will be lessened, but still a smudge.
If rate=0, formula resulted in nan. This is why small rate branch is needed.

Let EFF(i,n) = (1+i)^n - 1, but accurately evaluated using expm1/log1p

Effect is gradual, but this will still get in trouble with small rate.
If EFF(i,n) ≈ i*n, formulas (NPV,NPMT,NFV} totally breaks down.

f = NPMT/n = ((pv+fv)/EFF(i,n) + pv)*i + pmt ≈ (pv+fv+n*pmt)/n + pv*i

Without solving for f=0, formula cannot be correct.
Time reversed expression give different slope (+pi --> -fv), which make no sense.
BTW, these slopes are from i=∞ and -1, completely opposite of small rate!

With small rate formula, {n,pv,fv} ↔ {-n,-fv,-pv} time reversal make no difference.

f = (pv+fv+n*pmt)/n + ((pv+fv)/n+(pv-fv))/2*i + (pv+fv)/n*(n²-1)/12*i^2 + ...