Some TVM fun

[Albert Chan]

(01-03-2024 08:10 PM)dm319 Wrote:  And in part VI Plus42 is the only one that finds the negative root first. Is that because it is only going left?

TVM problems with 2 sign changes, we may have 2 rate solutions, from rate edges [PMT/-PV, PMT/FV]
Thomas wanted solver to always give one rate, and decided smallest absolute edge for rate guess.

Think of a huge loan, after some payments, with a small left-over (future value sign unknown)
It is reasonable to assume user wanted the rate close to future value = 0, and not the other.

Here is Part VI 2 rate roots, solved with Plus42 equations.
I keep this around, just in case I need the other rates, or both.

TVM:0=(1/EXPM1(N*LNP1(I))*(PV+0*PMT+FV)+PV+BEGIN*PMT)*I+PMT

XEQ "EQN", pick above. Set N=10, PV=50, PMT=-30, FV=80, BEGIN=0

If guess I = PMT/FV = -0.375, we get I ≈ −0.3689
If guess I = PMT/-PV = 0.600, we get I ≈ +0.5846      (*)

Note that solved rates are always inside rate edges.

(*) solver actually take 2 guesses. One stored previously, the other just entered.
To make sure only edge guess used, enter it twice! 0.6 [I] [ENTER] [I] [I] to solve