weeks 10 & 11

# weeks 10 & 11 - 4/30/2009 Learningobjectives...

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4/30/2009 1 Teaching Weeks 10 & 11 Introduction to Financial Mathematics Readings: Chapter 10–Prescribed text Learning objectives Explain the concept of the time value of money Calculate the future and present value of single sum and mixed stream cash flows using both simple and compound interest Plot cash flows on a timeline Explain the benefits of compounding Solve financial mathematics problems that require calculation of the number of periods or the interest rate Time value of money Time value of money Motivating question You have \$100 and are given two options as to what to do with it. First, you could put it under your bed for a year Second you could invest it in your bed for a year. Second, you could invest it in a bank for the year. What should you do? Why? Time value of money Answer You should put the money in the bank Why? Because you can earn interest on your investment Time value of money Assume that you can invest at 8% per annum How much will the \$100 be worth in one year’s time? \$108

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4/30/2009 2 Time value of money Therefore, \$100 today is not worth \$100 in one year’s time In fact, if interest rates are 8% per annum \$100 today is worth \$108 in one year’s time Why? Because money has time value Time value of money The concept that money has value due to time because any money received now or in the past can be invested to earn interest The implication of money having time value is that \$1 is worth more (less) the sooner (later) it is received, all other things being equal Time value of money Consequence of money having time value You cannot add amounts at different points in time If you have \$100 today and will receive \$100 in one year’s time, this does not mean that you have \$200 in total Time value of money Why? If interest rates are 8% per annum, \$100 today is actually worth \$108 in one year’s time So, \$100 today and \$100 in one year’s time is actually worth \$208 in one year’s time A consequence of money having time value is that you can only add amounts at the same point in time Interest rate Interest is the amount of money earned on a financial contract in the form of debt The distinguishing feature of debt is that one party to the transaction (the borrower) makes a specific promise to the other party to the transaction (the lender) about the payment of future cash flows Interest rate With the \$100 bank investment, the bank as the borrower agrees to pay you the lender \$108 in one year’s time However the bank will not state explicitly that it However, the bank will not state explicitly that it will pay you \$108 in one year’s time; instead it will state the rate of interest (8% p.a.) that it will pay you on your investment Hence, the interest rate is the rate of return earned on debt
4/30/2009 3 Rate of return More generally, the rate of return is the percentage return on an investment on any financial contract I.e. not necessarily a debt contract

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## This note was uploaded on 07/19/2011 for the course BUS 1000 taught by Professor Chalmers during the One '11 term at Monash.

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weeks 10 & 11 - 4/30/2009 Learningobjectives...

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