Looking for TVM contributions

[Albert Chan]

(06-17-2024 09:03 PM)robve Wrote:  Assuming TYPE is 0 for END and 1 for BGN, then we recognize PV and FV are switched and their signs inverted and N is inverted:
PV*S + PMT*K*R/I + FV = 0
with K=1+B*I and R=EXPM1(-N*LNP1(I)) and S=R+1

Compare this to

FV = (K*PMT*R/I-PV)/S
K*PMT*R/I - PV - FV*S = 0

This gives the same TVM problem.

Time reversed NFV turns into NPV, and vice versa.
We are solving same problem, but curve totally different.

(05-31-2024 10:39 PM)Albert Chan Wrote:  10 B=1 @ N=40 @ P=900 @ M=-40 @ F=-1000
20 DEF FNF(I) @ S=(1+I)^(-N) @ U=(1-S)/I @ K=1+B*I
30 FNF=P+K*M*U+F*S @ END DEF ! NPV
40 V=.01 @ W=FNF(V) @ I=.02 @ Y=FNF(I)
50 H=I-V @ V=I @ I=I-H*Y/(Y-W) @ W=Y @ Y=FNF(I)
60 DISP 100*I,Y @ IF V/I+I/V<>2 THEN 50

>run
 3.55877069046      -223.49575008
 4.3407684864        -68.532154113
 4.68660450765      -10.546204073
 4.74950349013      -.604877167
 4.75333056057      -.005731135
 4.75336716844      -.000003149
 4.75336718857      -.000000001

Let's turn NPV into NFV for rate problem, by time-reversal.

>15 VARSWAP P,F @ M=-M @ N=-N
>run
 11.3570289363       36923.539379
 2.35993812666      -1387.63023153
 2.68581267787      -1287.38125489
 6.87064131886       3585.77746844
 3.79135227821      -769.04731268
 4.33514429757      -379.62865086
 4.86526534953       115.24756927
 4.7418099072        -11.55575603
 4.75306056619      -.30740914
 4.75336803852       .00085219
 4.75336718851      -.00000007

Very unstable with multiple overshoot. NFV (n>0) formula for rate not recommended