2011_Week_2_-_The_Time_Value_of_Money_-_An_Introduction_to_Financial_Mathematics.ppt

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2011_Week_2_-_The_Time_Value_of_Money_-_An_Introduction_to_Financial_Mathematics.ppt

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2011_Week_2_-_The_Time_Value_of_Money_-_An_Introduction_to_Financial_Mathematics

Financial Markets and SystemsLecture 2 The Time Value of Money: An Introduction to Financial Mathematics 1. Lecture Overview This week will provide you with an introduction to financial mathematics. The lecture is designed to ensure you have the tools necessary to calculate the value of financial instruments later in the course. Today’s lecture will consider: Why a dollar received today is worth more than a dollar received any time after today; and, How to calculate what a dollar received at some time in the future is worth today. 2. The Time Value of Money If we receive $1 today we can invest it, earn interest and end up with more than $1 at any time in the future. Given this, if offered the choice, you would prefer receiving $1 today over receiving $1 at some future date. 2.1 Future Value of a Single Cash Flow In exploring the idea that $1 today is worth more than $1 received in the future, consider how you could invest $1 received today and end up with greater than $1 at some future date. Example 1: We received $1 today and decided to deposit it in the bank for a period of 2 years. If, during this time, the $1 earns interest at a rate of 10% per annum (calculated at the end of each year), what is it’s value in 2 years’ time? 2.1 Future Value of a Single Cash Flow Solution: This question is asking us to calculate the future value (ie the worth of the asset at some future date). The answer to this question depends on whether we use simple interest or compound interest calculations: Simple Interest: The amount of interest paid is only a function of the initial principal invested (ie if the principal doesn’t change then, given a constant interest rate, the interest paid each period will be the same); and, Compound Interest: Interest in successive periods is calculated based on the principal as well as on interest earned in previous periods (ie interest is earned on interest). 2.1 Future Value of a Single Cash Flow Solution Using Simple Interest Calcu