(11C) TVM for HP-11C

[Albert Chan]

(12-06-2020 02:32 PM)Albert Chan Wrote:  For fv_i() problems, where PV=0, add negative sign for the input.
In other words, fv_i(n, a) ≡ pv_i(-n, -a)

Proof:

Let K = (1+I)^N. TVM equation (NFV = 0):

PV*K + PMT*(K-1)/I + FV = 0

Travel backward in time: (N, PV, PMT, FV) := (-N, FV, -PMT, PV)

FV/K - PMT*(1/K-1)/I + PV = 0

Multiply by K, we recover the original TVM equation.

⇒ fv_i(n, a) = fv_i(n, FV/-PMT) = pv_i(-n, PV/PMT) = pv_i(-n, -a)

Since guess_i() is based on TVM, it can travel backward in time too.
Example taken from Fun Math Algorithms, car lease APR estimate.

lua> n, pv, pmt, fv = 36, 30000, -550, -15000
lua> guess_i(n, pv, pmt, fv) * 1200
6.9657545218584485
lua> guess_i(-n, fv, -pmt, pv) * 1200
6.9657545218584485

Update: numbers adjusted with updated guess_i()