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Lecture_2_-_The_Time_Value_of_Money_-_An_Introduction_to_Financial_Mathematics

# Lecture_2_-_The_Time_Value_of_Money_-_An_Introduction_to_Financial_Mathematics

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Money Markets and Finance Lecture 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 z If we receive \$1 today we can invest it, earn interest and end up with more than \$1 at any time in the future. z 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 Calculations: Future Value = Principal + interest FV = F 0 + F 0 r s n = F 0 (1 + r s n) = \$1 (1 + [0.1*2]) = \$1.20

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2.1 Future Value of a Single Cash Flow Solution Using Compound Interest Calculations: Future Value = F 0 (1 + r) n FV = \$1 (1 .1) 2 = \$1.21 Comparing the two answers, we can see the future value using compound interest is 1c more than if we use simple interest. Why? Because, with the compound interest, interest in the second period included an amount earned on the interest we were paid in the first period (ie in the second period, we earned 10% interest on the \$0.10 interest from the first period, or an extra 1c). 2.2 Present Value of a Single Cash Flow Using the time value of money idea, we also know that we would have to put an amount less than \$1 in the bank in order to receive \$1 from the investment in the future. Exactly how much less than \$1 we would need to deposit in the bank initially depends on: How long we are going to leave it there; and, How much interest we will earn in the mean time.
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Lecture_2_-_The_Time_Value_of_Money_-_An_Introduction_to_Financial_Mathematics

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