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On The Differences Among "Equivalent" Loan Payment Plans

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2010 Annual Conference & Exposition


Louisville, Kentucky

Publication Date

June 20, 2010

Start Date

June 20, 2010

End Date

June 23, 2010



Conference Session

Frontiers in Engineering Economy

Tagged Division

Engineering Economy

Page Count


Page Numbers

15.924.1 - 15.924.22



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Paper Authors


John White University of Arkansas

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John A. White, PhD, PE, is Distinguished Professor and Chancellor Emeritus at the University of Arkansas. ASEE Fellow, IIE Fellow and Past-President, INFORMS Fellow, member of the National Academy of Engineering, Past-Chairman of AAES, Past-President of the Malcolm Baldrige National Quality Award Foundation, Past-President of the National Consortium for Graduate Degrees for Minorities in Engineering and Science, and former Assistant Director for Engineering at NSF, former Dean of Engineering at Georgia Tech, he served on the boards of directors for 5 publicly traded corporations and served two 6-year terms on the National Science Board. Recipient of numerous awards, his primary professional interests are in economic analysis, facilities planning, and logistics.

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Kenneth Case Oklahoma State University

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Kenneth E. Case, PhD, PE, is Regents Professor Emeritus of Industrial Engineering and Management at Oklahoma State University. Named Outstanding Engineer in Oklahoma in 1987, he has served as Senior Examiner and on the Panel of Judges for the Malcolm Baldrige National Quality Award. Past-President and Fellow of the Institute of Industrial Engineers, Past-President and Fellow of the American Society for Quality, and member of the National Academy of Engineering, he is the recipient of numerous prestigious awards and has published numerous papers and books. A consultant to a wide variety of organizations, his primary professional interests are in quality and reliability engineering and economic analysis. Active in scouting, he has received the Distinguished Eagle Scout and Silver Bear medals.

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David Pratt Oklahoma State University

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David B. Pratt, PhD, PE, is Associate Professor and Director of the Undergraduate Program in the School of Industrial Engineering and Management at Oklahoma State University. An APICS Certified Fellow in Production and Inventory Management and an ASQ Certified Quality Engineer, he held technical and managerial positions in the aerospace, petroleum, and pulp and paper industries prior to joining the OSU faculty. A member of APICS, ASQ, IIE, INFORMS, and NSPE, his professional interests include economic analysis, manufacturing systems design, and production planning and control.

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract


Throughout its many editions, Principles of Engineering Economy, by Eugene L. Grant and, subsequently, in partnership with W. Grant Ireson and Richard S. Leavenworth, provides an example in which a loan can be repaid using one of four different plans: I (interest payments only until the end of the loan period, at which time the principal is repaid); II (equal principal payments, plus interest on the unpaid balance of the loan); III (equal periodic payments); and IV (single payment of principal and accumulated interest at the end of the loan period). These and similar payment plans appear in a number of other books.1,4,5,6 Insofar as the lender is concerned, the four payment plans are identical to the

Here, we explore differences among the four payment plans from both the and the lende perspectives. Sensitivity analyses are performed for the various payment plans and conclusions are drawn regarding the plans that maximize -tax present worth -tax present worth in an inflationary economy.

Interestingly, the payment plan that is emphasized in engineering economy courses and found to be most prevalent in practice, a uniform series of loan payments, does not perform as well as other plans when considered from either or the lende perspective. Further, the performance of the fourth plan (a lump-sum payment at the end of the loan period) is radically

value of money. From the analysis, it is evident that neither the borrower nor the lender should be indifferent when choosing a payment plan from among those considered.


In the early editions of Principles of Engineering Economy,2 four plans were presented for repaying a $10,000 loan in 10 years with interest at 6%. Plan I consisted of 10 equal annual interest payments of $600 and a $10,000 payment at the end of 10 years. Plan II consisted of 10 equal annual principal payments of $1,000, plus interest payments on the unpaid principal balance. Plan III, the familiar equal-annual-payment plan, consisted of 10 equal annual payments of $1,358.68. Plan IV consisted of a single payment of $17,908.49 after 10 years.

As subsequent editions were published, the interest rate in the example changed to reflect economic conditions at the time of publication. The most recent edition3 uses a rate of 9%. Accompanying the discussion of the example, the present worth of each plan is computed using a range of interest rates; again, the range of rates changed over the years. The point is made that the four plans are equivalent only at the stated interest rate, a rate which we refer to as the equivalent rate.

As we studied the results of the calculations involving a range of interest rates, we noted that the rank ordering of present worth values (from largest to smallest) was Plan IV, Plan I, Plan III, and Plan II when the interest rate was less than the equivalent rate. However, the rank ordering was

White, J., & Case, K., & Pratt, D. (2010, June), On The Differences Among "Equivalent" Loan Payment Plans Paper presented at 2010 Annual Conference & Exposition, Louisville, Kentucky. 10.18260/1-2--15915

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