Lecture6_Oct24_2005

Lecture6_Oct24_2005 - EMP5100 - Introduction to Engineering...

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EMP5100 - Introduction to Engineering Management Lecture 6 6. Techniques for making better Engineering Management Decisions(cont.) Cash Flow Analysis Techniques (cont.) Compound interest (cont.) Compound interest: I = A – P Present Value: P = A/(1+i)**n = A * (1+i)**(-n) Definitions: An Annuity : This is a sequence of equal periodic payment Payment period : The length in time between two successive payments is called the payment period or payment interval. Term of Annuity : The length of time between the beginning of the first payment period and the end of the last payment period is called the term of annuity Annual Rent : the sum of payments made in one year is the annual rent. The Amount of Annuity This is the sum of the compound amounts which would be obtained if each payment when due were kept at interest until the end of the specified term. 0 1 2 3 4 time(years) |---------+---------+---------+---------+---------+-------- $0 $100 $200 $300 $400 Amount A at the end of the first year will be zero until the depositor adds amount A. At the end of the second year: A t = A*(1+i) To this depositor adds an amount ‘A’: A t = A*(1+i)+A At the end of the 3 rd year: A t = [A*(1+i)+A](1+i)+A A t = A*(1+i)**2+A*(1+i)+A At the end of the n th year: A t = A(1+i)**(n-1)+…+A(1+i)+A A t = A*[1+(1+i)+(1+i)**2+…+(1+i)**(n-1)] (equation 1) This is a Geometric Series. (1+i) A t = A[(1+i)+(1+i)**2+…+(1+i)**n] (equation 2) Subtract eq.1 from eq.2: (1+i) A t - A t = A[(1+i)**n-1] A t = A*[(1+i)**n - 1]/i EMP5100 1 October 24, 2005
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EMP5100 - Introduction to Engineering Management Lecture 6 The present value of Annuity This is the sum of the payment values of all payments. Consider now the problem of computing present value of a payment of amount ‘A’ to be
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Lecture6_Oct24_2005 - EMP5100 - Introduction to Engineering...

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