MSci261-2007-Ch_2 - Chapter 2 Time value of money MSci 261...

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Chapter 2 1 Chapter 2 Chapter 2 MSci 261: Managerial and Engineering Economics Spring 2007 Instructor: Bon Koo Time value of money Time value of money
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Chapter 2 2 Motivation of the chapter Motivation of the chapter The costs and benefits of a project occur at different times E.g., invest today and obtain profits in the future However, we need to compare them at the same period, by converting future benefit into the present value, or converting current cost into the future value. Interest rate is the key for this conversion. In this chapter, we will learn the concept of interest rate and how to convert values in different times using the interest rate.
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Chapter 2 3 1. Interest and interest rate (1) 1. Interest and interest rate (1) Interest : the compensation for giving up the present use of money for the duration of a loan $100 now vs. $100 next year?: People prefer $100 now. Need a compensation to make someone take $100 in the future The amount of the compensation is interest. This amount is needed even without inflation . Interest rate : the rate to calculate the amount of compensation Use percentage to normalize the different amount of interest.
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Chapter 2 4 1. Interest and interest rate (2) 1. Interest and interest rate (2) An amount of money today, P, can be related to a future amount, F, by the interest rate i: F = P + I = P + iP = P(1 + i)
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Chapter 2 5 Example 1-1: Interest Example 1-1: Interest Sam borrowed $5,000 from a bank last year. How much does he pay to the bank a year later if the interest rate is 10%? P = $5,000; i = 0.1 F = P(1 + i) = 5000(1 + 0.1) = $5,500 $5,000 is the principal amount and $500 is the interest. P is called present worth and F is future worth.
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Chapter 2 6 Example 1-2: Interest Example 1-2: Interest Beth borrowed $20,000 to pay for a college education. How much does she pay to the bank four years later if the interest rate is 10%?
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