TVM solve for interest rate, revisited

[Albert Chan]

(06-23-2022 07:04 PM)Albert Chan Wrote:  if abs(pv) > abs(fv) then n,pv,fv = -n,-fv,-pv end

An example to show improvement by keeping |pv| small.

f = 0      ⇒ -pmt/x = (pv+fv)/expm1(log1p(x)*n) + pv

Plus42 TVM, P/YR=1, END mode. Solve for I, then use it to solve back PMT

N, PV, PMT, FV = 10, 1E10, 10, -100
I%/YR --> -84.34981140003005709231099197156087
PMT ----->  9.999999999999999999999999899268213

N, PV, PMT, FV = -10, 100, 10, -1E10
I%/YR --> -84.34981140003005709231099197367593
PMT ----->  9.999999999999999999999999999999781

Update 6/27/24 Plus42 PMT changed.
Solve for PMT or I%YR prefer small sized PV.
Solve for PV or FV prefer negative n.
Solve for N prefer small sized FV.

I wish Plus42 result does not get affected by time-symmetry.

N, PV, PMT, FV = -10, 100, 10, -1E10
I%YR = -84.34981140003005709231099197156087
PMT -->  9.999999999999999999999999899268215
I%YR = -84.34981140003005709231099197367593
PMT -->  9.999999999999999999999999999999791