1. Math 1140 Financial Mathematics Lecture 5 Equations of Value Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.edu/~ans5k/

2. Math 1140 - Financial Mathematics Homework comments Some of you really tried to understand the details of you credit card agreement. Most of you did not. I got some great answers in the last problem. The return on investment is not realistic! “… which method is more advantageous totally depends on the risk and stock quality” 2

3. Math 1140 - Financial Mathematics McDonalds 3

4. Math 1140 - Financial Mathematics Best Buy 4

5. Math 1140 - Financial Mathematics Projects Based on the second homework quality I am anticipating very interesting projects. Start thinking about what you would like to do and with whom! 5

6. Math 1140 - Financial Mathematics Homework 3 For exercises 2, 4, 5 calculate the term using months! If you find my typed version confusing, use the textbook! 6

7. Math 1140 - Financial Mathematics Questions? 7

8. Math 1140 - Financial Mathematics Terms from last time Add-on loan Discount for prompt payment 8

9. Math 1140 - Financial Mathematics Maturity(Future) Value 9

10. Math 1140 - Financial Mathematics Present Value We know the term, interest rate and the maturity value (future value). We want to know how much we need to invest today. 10

11. Math 1140 - Financial Mathematics Present and Future Value Your grandma sends you a $500 check for your birthday. What is the value of the $500 on your birthday? 11 What is the value of the $500 four years from now?

12. Math 1140 - Financial Mathematics Past value What was the value of the $500 four years ago? A)0 B)$500 C)More than $500 D)Less than $500 This is a participation question. 12

13. Math 1140 - Financial Mathematics Let’s see What was the value of the $500 four years ago? is the same as How much money would you have had to invest four years ago? 13

14. Math 1140 - Financial Mathematics Conclusion Money has value at all times – now, in the past and in the future. 14

15. Math 1140 - Financial Mathematics Fourteenth Amendment Section 4. The validity of the public debt of the United States, authorized by law, including debts incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion, shall not be questioned. But neither the United States nor any State shall assume or pay any debt or obligation incurred in aid of insurrection or rebellion against the United States, or any claim for the loss or emancipation of any slave; but all such debts, obligations and claims shall be held illegal and void. 15

16. Math 1140 - Financial Mathematics Why is the US Capital where it is? 16

17. Math 1140 - Financial Mathematics 17 This broke out on every question with the most alarming heat, the bitterest animosities seemed to be engendered, and tho’ they met every day, little or nothing could be done from mutual distrust and antipathy.... It ended in Mr. Madison’s acquiescence in a proposition that the question should be again brought before the House by way of amendment from the Senate, that tho’ he would not vote for it, nor entirely withdraw his opposition, yet he should not be strenuous, but leave it to its fate. It was observed, I forget by which of them, that as the pill would be a bitter one to the Southern states, something should be done to soothe them; that the removal of the seat of government to the Potomac was a just measure, and would probably be a popular one with them, and would be a proper one to follow the assumption. Thomas Jefferson, Memorandum on the Compromise of 1790

18. Math 1140 - Financial Mathematics Simple Debt Instruments A debt instrument is a legal document showing evidence of a debt. 18

19. Math 1140 - Financial Mathematics Promissory Note A legal document specifying the terms of a loan: the principal the terms of repayments the interest rate the date the maturity date Different from IOU and loan contract. 19

20. Math 1140 - Financial Mathematics Discounting the note A debt instrument can be sold for less than the maturity value. This is called discounting the note. The terms of the loan do not change for the borrower. 20

21. Math 1140 - Financial Mathematics Possible Scenario A subprime borrower takes out a simple interest rate loan from Shady Bank with a certain maturity date and interest rate. Shady Bank decides the risk is too high and sells the loan to the Unsuspecting Investor who wants a higher interest rate. The problem is to calculate the sell price. 21

22. Math 1140 - Financial Mathematics Given data P – the principal i 1 – the original interest rate of the loan d 1 – the date of the loan d 3 – the maturity date i 2 – the interest rate desired by the buyer of the loan d 2 – the sale date 22

23. Math 1140 - Financial Mathematics Unknown P 2 – the price Unsuspecting Investor pays to Shady Bank 23

24. Math 1140 - Financial Mathematics Solution Step 1 - Calculate the maturity value 24 We use the formula for future value: S = P( 1 + i 1 t 1 ) t 1 is the (exact) time from d 1 to d 3 S is the value of the principal at time d 3

25. Math 1140 - Financial Mathematics Solution Step 2 – Discount the maturity value This means to calculate the present value at time d 2 25 We use the formula for present value:

26. Math 1140 - Financial Mathematics Example Bob holds a promissory note signed by Alice on 23 August 2011. The note is for $1,000 at 12% simple interest with a maturity date of 23 March 2012. On 23 December 2011, Bob sells the note to Katie who wants 15% simple interest. 26

27. Math 1140 - Financial Mathematics Solution 27

28. Math 1140 - Financial Mathematics Equations of Value A focal date is a chosen date to evaluate the money. An equation of value is a mathematical expression involving several pieces of money at a focal date. 28

29. Math 1140 - Financial Mathematics The Golden Rule of Finance Monies cannot be added or reconciled unless they are valued at the same point in time. 29

30. Math 1140 - Financial Mathematics Investments Goal: predict if an investment will give a good rate of return. The rate of return of an investment is the ratio of money gain or lost relative to the money invested. 30

31. Math 1140 - Financial Mathematics Example You win the darts contest at your favorite watering hole and have a choice of how to receive your prize. Option 1: $750 now Option 2: $500 in three years and $550 in seven years If money can be invested at 10% simple interest which option would you choose? 31

32. Math 1140 - Financial Mathematics Solution 32

33. Math 1140 - Financial Mathematics Charge Due Monday: Read section 1.9 Due Wednesday : Third homework 33