(17B/19B) GPM: initial payment

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An excerpt from The Graduated Payment Mortgage: Solving the Initial Payment Enigma, , Journal of Real Estate Practice and Education, vol. 1, no. 1, 1998, pp. 67-79 73

APPLICATION OF THE GPM GENERALIZED EQUATION
The generalized GPM equation given in equation (9) is best implemented using a programmable calculator such as the Hewlett Packard (HP) 17B (or HP19B) or a spreadsheet such as Lotus 1-2-3 or Microsoft Excel. For the HP 17B, the user needs to enter into the equation solver in the main menu (SOLVE) and create the following new equation (NEW) as one line (spaces are ignored by SOLVE):
GPM = PV ÷ ((∑(T:1:N-1:1:SPFV(G:T) ÷ SPFV(I:12XT))+1)X
                     USPV((I:12) + SPFV(G:N) ÷ SPFV(I:12XN)X
                     USPV(I:(12XM) - (12XN)))
Once entered correctly, the user should press CALC in the SOLVE menu to verify the equation. The user then enters PV, N, G, i, and M. It should be noted that N and M are in years, G is annual interest rate, and i is a monthly interest rate. As an alternative to the one-step approach, the user can define the term in parentheses as the graduated annuity interest factor (GAIF) and then do a second equation that defines the GPM as PV/GAIF; the HP 17B and HP 19B automatically store the GAIF value from the first step. The advantage of the two-step approach is that the GAIF can be used separately, for example, to find the present value of a loan.

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