(17B) Graduated Payment Mortgage

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An extract 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.

Abstract:
Executive Summary: The graduated-payment mortgage (GPM) has a unique stair-step payment schedule that often enhances borrower qualification for young, first-time home buyers who are anticipated to have increasing incomes. The determination of the initial payment on a GPM mortgage is often regarded as complex; therefore, textbook authors normally disregard its theoretical development and substitute instead GPM interest factor tables. This study develops a general equation for finding the initial payment on a GPM and programmable calculator and computer spreadsheet routines for implementing the general equation. This approach enhances the technical understanding of the GPM, and it offers more flexibility than a table approach.
Article:
INTRODUCTION
The graduated-payment mortgage (GPM) was designed in the mid-1970s as an alternative to a fixed-rate mortgage; the primary motivation for its development was an effort by the Department of Housing and Urban Development to lower monthly mortgage loan payments during the first few years following a loan's inception. The stair-step payment schedule of a GPM often improves borrower qualification …
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The purpose of this article is to demonstrate the development of a generalized equation for finding the initial GPM payment, and routines for implementing the generalized equation using a programmable calculator or computer spreadsheet. For a pedagogical perspective, we develop the graduated-payment solution through a Time Value of Money (TVM) approach …
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This substitution permits the solution by use of a scientific calculator.
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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):
… equation listing …
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 …

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