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Solution to exchanges 10.2 puzzle: borrowing in the limit as our nerdiness goes to infinity

Solution to exchanges 10.2 puzzle: borrowing in the limit as our nerdiness goes to infinity Solution to Exchanges 10.2 Puzzle: Borrowing in the Limit as our Nerdiness Goes to In nity RAN I. SHORRER Harvard University and Harvard Business School This is a solution to the editor ™s puzzle from issue 10.2 of SIGecom Exchanges [Reeves 2011]. The Puzzle asks to determine a point in time such that a lump sum payment of $S will be equivalent to a continuous stream of in nitesimal payments totaling $S, spread evenly over time. The full puzzle can be found online at: http://www.sigecom.org/exchanges/volume 10/2/puzzle.pdf. Categories and Subject Descriptors: J.4 [SOCIAL AND BEHAVIORAL SCIENCES]: Economics General Terms: Economics Additional Key Words and Phrases: Interest The puzzle asks to determine a point in time such that a lump sum payment of $S will be equivalent to a continuous stream of in nitesimal payments totaling $S, spread evenly over an amount of time T. This note presents a short solution and some of my intuitions.1 In the spirit of the puzzle, I start with an illustration of the nature of the annualized interest rate. Let r be the annualized interest rate. If the rate of interest is xed, the semiannual rate r2 is such that (1 + r2 )2 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGecom Exchanges Association for Computing Machinery

Solution to exchanges 10.2 puzzle: borrowing in the limit as our nerdiness goes to infinity

ACM SIGecom Exchanges , Volume 11 (1) – Jun 1, 2012

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2012 by ACM Inc.
ISSN
1551-9031
DOI
10.1145/2325713.2325721
Publisher site
See Article on Publisher Site

Abstract

Solution to Exchanges 10.2 Puzzle: Borrowing in the Limit as our Nerdiness Goes to In nity RAN I. SHORRER Harvard University and Harvard Business School This is a solution to the editor ™s puzzle from issue 10.2 of SIGecom Exchanges [Reeves 2011]. The Puzzle asks to determine a point in time such that a lump sum payment of $S will be equivalent to a continuous stream of in nitesimal payments totaling $S, spread evenly over time. The full puzzle can be found online at: http://www.sigecom.org/exchanges/volume 10/2/puzzle.pdf. Categories and Subject Descriptors: J.4 [SOCIAL AND BEHAVIORAL SCIENCES]: Economics General Terms: Economics Additional Key Words and Phrases: Interest The puzzle asks to determine a point in time such that a lump sum payment of $S will be equivalent to a continuous stream of in nitesimal payments totaling $S, spread evenly over an amount of time T. This note presents a short solution and some of my intuitions.1 In the spirit of the puzzle, I start with an illustration of the nature of the annualized interest rate. Let r be the annualized interest rate. If the rate of interest is xed, the semiannual rate r2 is such that (1 + r2 )2

Journal

ACM SIGecom ExchangesAssociation for Computing Machinery

Published: Jun 1, 2012

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