Financial and Insurance Formulas
This survey contains more than 3,000 formulas and methods from the field of finance and insurance mathematics (as well as related formulas in mathematics, probability theory, statistics, econometrics, index numbers, demography, stochastic processes and ti
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Tomas Cipra
Financial and Insurance Formulas
Tomas Cipra Charles University of Prague Dept. of Statistics Faculty of Mathematics and Physics Sokolovska 83 186 75 Prague Czech Republic [email protected]
ISBN 978-3-7908-2592-3 e-ISBN 978-3-7908-2593-0 DOI 10.1007/978-3-7908-2593-0 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010925641 © Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Printed on acid-free paper Physica-Verlag is a brand of Springer-Verlag Berlin Heidelberg Springer-Verlag is part of Springer Science+Business Media (www.springer.com)
To my wife and parents
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part I
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Financial Formulas
2 Simple Interest and Discount . . . . . . . . . . . . 2.1 Simple Interest . . . . . . . . . . . . . . . . 2.2 Calendar Conventions . . . . . . . . . . . . . 2.3 Simple Interest with Principals Credited mthly 2.4 Simple Discount . . . . . . . . . . . . . . . . Further Reading . . . . . . . . . . . . . . . . . . . .
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3 Compound Interest and Discount . . . . . . . . . . . . . 3.1 Compound Interest . . . . . . . . . . . . . . . . . 3.2 Compound Discount . . . . . . . . . . . . . . . . 3.3 Compound Interest and Discount Convertible mthly 3.4 Combination of Simple and Compound Interest . . Further Reading . . . . . . . . . . . . . . . . . . . . . . .
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11 11 12 13 15 16
4 Continuous Interest and Discount . . . . . . . . . . . . . . . . . . . Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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5 Classical Analysis of Interest Rates . . . . . . . . . 5.1 Risk-Free Interest Rate and Real Interest Rate 5.2 Term Structure of Interest Rates . . . . . . . Further Reading . . . . . . . . . . . . . . . . . . . .
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6 Systems of Cash Flows . . . . . 6.1 Present and Future Value 6.2 Internal Rate of Return . 6.3 Payback Period . . . . . 6.4 Duration . . . . . . . . . 6.5
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