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Unformatted text preview: Future Value and Present Value Standard Annuity Modified annuities Conclusion Ch5. The time value of money JHT Kim ActSc 371 January 27, 2009 1/26 Future Value and Present Value Standard Annuity Modified annuities Conclusion Notations Different texts use different terminology in interest theory. In this course (including this chapter): Discount rate is the same as interest rate Nominal rate of interest is the same as the Annual Percentage Rate (APR) 2/26 Future Value and Present Value Standard Annuity Modified annuities Conclusion Future Value If your invest A at an annual rate of r (100r%), the FV in your acct in one year is A (1 + r ) This can be split into the principal A and the interest amount earned A (1 + r ) A = Ar . The FV in n yrs is A (1 + r ) n and can again be split into principal A and the interest amount A (1 + r ) n A 3/26 Future Value and Present Value Standard Annuity Modified annuities Conclusion Present Value Suppose your bank offers you an annual interest rate of r . If you want your FV to be B in one yr the amount you need to invest now is B / (1 + r ) We call 1 / (1 + r ) the discount factor or the PV factor. Since we use this quite often we denote 1 / (1 + r ) by v . If you want the FV to be B in n yrs, your initial investment amount now (or PV) should be PV = B / (1 + r ) n = Bv n Note: the text uses term NPV when there are initial costs, but we will use them interchangeably. 4/26 Future Value and Present Value Standard Annuity Modified annuities Conclusion Present Value Example You can invest in a project with $ B now to get $ B 1 in one year from now and $ B 2 in 2 yrs. Compute the NPV of this project at an annual rate of r. 5/26 Future Value and Present Value Standard Annuity Modified annuities Conclusion NPV principle For a project (say, A) If NPV(A) is positive ⇒ should undertake the project (value created) If NPV(A) is negative ⇒ should forgo the project (value cutback) For two projects (A and B), assuming only one of the two can be chosen, If NPV(A) > NPV(B) ⇒ should choose A If NPV(A) < NPV(B) ⇒ should choose B 6/26 Future Value and Present Value Standard Annuity Modified annuities Conclusion Definition of annuity An annuity is a series of payments that lasts for a fixed number of periods. Consider an annuity that has the following payment pattern: We use an actuarial symbol for the PV of this annuity. That is, a n  r = 1 (1 + r ) + 1 (1 + r ) 2 + ... + 1 (1 + r ) n = v + v 2 + ... + v n We can simplify this (how?) to arrive at an imprtant formula a n  r = 1 v n r 7/26 Future Value and Present Value Standard Annuity Modified annuities Conclusion Notation a n  r is commonly called the annuity factor (text uses...
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This note was uploaded on 04/24/2010 for the course ACTSC 371 taught by Professor Wood during the Spring '08 term at Waterloo.
 Spring '08
 Wood

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