Download e-book for kindle: An Introduction to Actuarial Mathematics by Arjun K. Gupta, Tamas Varga

By Arjun K. Gupta, Tamas Varga

ISBN-10: 9048159490

ISBN-13: 9789048159499

ISBN-10: 9401707111

ISBN-13: 9789401707114

to Actuarial arithmetic through A. ok. Gupta Bowling eco-friendly nation college, Bowling eco-friendly, Ohio, U. S. A. and T. Varga nationwide Pension assurance Fund. Budapest, Hungary SPRINGER-SCIENCE+BUSINESS MEDIA, B. V. A C. I. P. Catalogue list for this e-book is out there from the Library of Congress. ISBN 978-90-481-5949-9 ISBN 978-94-017-0711-4 (eBook) DOI 10. 1007/978-94-017-0711-4 revealed on acid-free paper All Rights Reserved © 2002 Springer Science+Business Media Dordrecht initially released by means of Kluwer educational Publishers in 2002 No a part of the cloth safe by means of this copyright discover might be reproduced or used in any shape or in any way, digital or mechanical, together with photocopying, recording or through any details garage and retrieval method, with out written permission from the copyright proprietor. To Alka, Mita, and Nisha AKG To Terezia and Julianna television desk OF CONTENTS PREFACE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix bankruptcy 1. monetary arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1. Compound curiosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 2. current price. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1. three. Annuities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . forty eight bankruptcy 2. MORTALITy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eighty 2. 1 Survival Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eighty 2. 2. Actuarial features of Mortality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eighty four 2. three. Mortality Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ninety eight bankruptcy three. lifestyles INSURANCES AND ANNUITIES . . . . . . . . . . . . . . . . . . . . . 112 three. 1. Stochastic money Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 three. 2. natural Endowments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . one hundred thirty three. three. existence Insurances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 three. four. Endowments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 three. five. lifestyles Annuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 bankruptcy four. charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 four. 1. web charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 four. 2. Gross charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Vll bankruptcy five. RESERVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 five. 1. internet top class Reserves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 five. 2. Mortality revenue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 five. three. converted Reserves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 solutions TO ODD-NuMBERED difficulties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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How much interest is paid if a) the interest is paid at the end of the year? b) the interest is paid at the beginning of the year? 03) = $15. 02913. 56. 11, we can see that d < i. It is always true that (29) since CHAPTER 1 22 Annual interest rates are almost always less than 100%. However, it can also happen that i > 100%; for example, in countries with a hyper inflation. 12. We can invest money at an annual rate of interest of 4% for one year. How much do we have to invest if we want the accumulation to be $500 after one year?

Now we drop the condition that M(to,t) be monotone increasing. Thus we can allow for negative payments, since M(toh) - M(tO,tl) is the payment made in the time interval from tl to t2. What is the present value of a continuous payment stream? Assume we are interested in the present value at to of the payment stream M(to,t), to ::; t ::; teo Let us divide the interval (to,te) into n subintervals by the points tl < t2 < ... < tn-I· Then, M(tO,ti+l) - M(tO,ti) is the payment made between times ti and ti+ 1, i = O,l, ...

Solution: We have to find the present value of the annuity on January 1, 1991. Since this is an annuity-due, the present value is PV = 500 ii 20l Since . 029126 and from (2) we get 1 )20 .. 3238. 90. 2. A loan of $5000 is taken out on January I, 1992. It has to be repaid by 15 equal installments payable yearly in advance. Based on an 8% annual rate of interest, determine the amount of the installments. Solution: Denoting the annual installment by X, we get the equation 5000 = Xii 15l from which it follows that 5000 X=..

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An Introduction to Actuarial Mathematics by Arjun K. Gupta, Tamas Varga


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