(17B/19B) GPM: initial payment

[Gil]

Introduction

As I could not fully, clearly understand the formulae given in the above posts, discovering here the GMT concept, I tried to formulate the exposed idea on my own way, based on the same example data:

PV+
{PMT×1.075^0 × [(v^12-1)/i /(1.01^12)^0)] +
PMT×1.075^1 × [(v^12-1)/i /((1.01^12)^1)] +
PMT×1.075^2 × [(v^12-1)/i /(1.01^12)^2)] +
PMT×1.075^3 × [(v^12-1)/i /(1.01^12)^3)] +
PMT×1.075^4 × [(v^12-1)/i /(1.01^12)^4)] +
PMT×1.075^5 × [(v^(360-12*5)-1)/i /(1.01^12)^5)]
} =0

PV+
{PMT×(v^12-1)/i ×[Sum, (1.075/1.01)^j, j=0..(5-1)] +
PMT×[v^(360-12×5)-1)/i]×(1.075/1.01^12)^5
}=0,
with v=1/1.01, i=0.01

and of course we find then PMT=-474.825.



Transposition to a more general TVM-Growth HP48-50G Solver program

I transposed the corresponding program, letting it have equally the more usual case without growing payments (I.Growing%=0 or number of Years for the Growing payments YG=0).

To check the case/example of Albert Chan and Karinne in another post, I included the possibility of having the number of compoundings/year, C.Y, ≠ number of payments/year, P.Y.

Besides, I added here the choice of the payments being made at the end of each period (variable END10=1) or at the beginning of each period (variable END10=0).

Finally, I gave also the possibility of having a remaining global amount FV to be still paid at the very end of the process, ie at the end of YTOT.


Use

Launch the Sover program by pressing its name TVM.G.

Enter, in the Solver, your values followed by the corresponding variable names as follows: 30 YTOT 12 I%Y 12 P.Y 12 C.Y 7.5 IG%Y NEXT-key 60000 PV 0 FV 1 END10.

Then press, always in the Solver, LeftShift P1 to get the value of the payments during the first year.

The following years, the payments will be increased (or not) according to your indications (the several calculations are not included in the result here) until reaching (or not) a constant value P.CST (LeftShift P.CST or RightShift P.CST).

Code:


\<<
  \<< YTOT I%Y + C.Y + P.Y + YG + IG%Y + PV + FV + END10 + DUP - I%Y 100. / C.Y / 1. + C.Y ^ P.Y INV \->NUM ^ DUP INV IG%Y 100. / 1. + \-> r v rg
    \<< YG IG%Y * 0. ==
      IF
      THEN YTOT 'YG' STO 1. 'rg' STO
      END PV + FV v P.Y ^ YTOT ^ * + 1. v P.Y ^ - r 1. - / 0. 0. YG 1. -
      FOR j rg r P.Y ^ / j ^ +
      NEXT * 1. v YTOT YG - P.Y * ^ - r 1. - / rg r P.Y ^ / YG ^ * + END10 1. == 1. r IFTE * P1 * + P1 rg YG ^ * 'P.CST' STO
    \>>
  \>> STEQ 30. MENU
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