1. Lecture 8 Discount Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.edu/~ans5k/ Math 1140 Financial Mathematics

2. Math 1140 - Financial Mathematics Homework 3 was: A)Too hard B)Hard C)Just right D)Easy E)Too easy 2

3. Math 1140 - Financial Mathematics I did not come to office hours because: A)The homework was easy. B)I can’t make it. C)I started too late. D)It’s siesta time. E)What are you talking about, I came to office hours. 3

4. Math 1140 - Financial Mathematics 4

5. Grading Scale Great job Good job Minor mistakes You have some studying to do. 5 Serious studying needed. Come to office hours Make an appointment to see me.

6. Math 1140 - Financial Mathematics Questions? 6

7. Math 1140 - Financial Mathematics Discount Interest 7 Amount = money borrowed Discount = charge for the use of money Proceeds = money received from the loan Discount rate = percent of the amount used to calculate the discount Term = length of the loan in units of time

8. Math 1140 - Financial Mathematics The Basic Discount Interest Formula D = Sdt Where D is the discount S is the amount (future value) d is the discount rate t is the term This is the formula for calculating the discount! 8

9. Math 1140 - Financial Mathematics P = S - D Where P is the proceeds D is the discount S is the amount (future value) Calculates how much the borrower receives. P = S - D = S - Sdt = S(1-dt) Discount Proceeds Formula 9

10. Math 1140 - Financial Mathematics The discount proceeds formula P = S(1-dt) A)Moves money in forward in time B)Moves money backwards in time C)Keeps the money put D)Moves the money to Walmart 10

11. Math 1140 - Financial Mathematics 11 The value of money that we know is the amount S. We calculate the proceeds P at the due date. Thus we are moving S backwards in time from the due date to the loan date.

12. Math 1140 - Financial Mathematics A security that matures in 6 months at $7,000 is sold at a discount rate of 10%. How much does the buyer pay? A) $7,368.42 B) $7,000 C) $6,650 D) I whish I know. E) Who cares? 12

13. Math 1140 - Financial Mathematics 13 A security that matures in 6 months at $7,000 is sold at a discount rate of 10%. How much does the buyer pay?

14. Math 1140 - Financial Mathematics Discount Proceeds Formula P = S(1-dt) Discount Amount Formula Calculates the amount( S ) given the proceeds( P ), the discount rate( d ), and the term(t). 14

15. Math 1140 - Financial Mathematics A)Crystal clear B)I’m fine C)Not so clear D)I have no idea what that is Discount Amount Formula 15

16. Math 1140 - Financial Mathematics The discount amount formula A)Moves money in forward in time B)Moves money backwards in time C)Keeps the money put D)Turns the money into cheese 16

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18. Math 1140 - Financial Mathematics Please don’t email me about things that you can find by asking one your classmates(eg where do I buy the clicker, where do I register my clicker,…) Please use email 1)to ask questions about lectures and homework 2) to let me know if something is going on with you 3)missing or misreported grades Email Communication 18

19. Math 1140 - Financial Mathematics Before class, I need to get my many toys ready. After class, I am tired and very unlikely to remember what you told me. Please email me. Office hours are your best bet that I will remember and record what you said. Oral Communication 19

20. Math 1140 - Financial Mathematics Discount interest loan with discount rate d, amount S, term t. The proceeds P = S(1-dt). What is the interest of a simple interest loan with principal equal to the proceeds, maturity value equal to the amount and same term? Discount vs Simple Interest 20

21. Math 1140 - Financial Mathematics What is the interest rate of a simple interest loan given the principal, the maturity value and the term? 21

22. Math 1140 - Financial Mathematics Coupon equivalent is the simple interest rate of a loan that charges the same interest as a given discount loan. Coupon Equivalent 22

23. Math 1140 - Financial Mathematics Find the coupon equivalence of a 12-week bank discount rate of 8%. Example 23

24. Math 1140 - Financial Mathematics A)Crystal clear B)I’m fine C)Not so clear D)I have no idea what that is Coupon Equivalent 24

25. Math 1140 - Financial Mathematics Find the term of a loan taken out in February 2011 and due in July 2011. Find the term of a loan taken out in February 2011 and due in January 2012. Calculating terms 25

26. Math 1140 - Financial Mathematics a ≡ b mod n if a and b give the same remainder when divided by n. a+b ≡ (a+b) mod n a-b ≡ (a-b) mod n 1 ≡ 4 mod 3 -1 ≡ 2 mod 3 1+5 ≡ 6 ≡ 0 mod 3 1-5 ≡ -4 ≡ 2 mod 3 Modular Arithmetic 26

27. Math 1140 - Financial Mathematics Find the term of a loan taken out in February 2011 and due in January 2012. Do mod 12 arithmetic. February is the second month. January is the first month. The term is 1-2 ≡ -1 ≡ 11 mod 12 How can we use it? 27

28. Math 1140 - Financial Mathematics Find the term of a loan taken out in February 2011 and due in January 2013. February is the second month. January is the first month. The term is 1-2 ≡ -1 ≡ 11 mod 12 Be careful 28

29. Math 1140 - Financial Mathematics Find the term of a loan taken out in February 2011 and due in January 2012. Do mod 12 arithmetic. February is the second month. January is the first month. The term is 1-2 ≡ -1 ≡ 11 mod 12 How can we use it? 29

30. Math 1140 - Financial Mathematics S = P(1+it) P = $10 i = 10% S(t) = 10(1+0.1t) Future value 30 Wolfram Alpha command plot [10(1+0.1t), {t, 0, 10}]

31. Math 1140 - Financial Mathematics S = $20 i = 10% Present value 31 Wolfram Alpha command plot [20/(1+0.1t), {t, 0, 10}]

32. Math 1140 - Financial Mathematics plot [14.4/(1+0.1t), 10(1+0.1t), {t, 0, 10}] 32

33. Math 1140 - Financial Mathematics Compare the values: 1)Money moved 1 year forward 2) Same money moved forward two years and then move them one year backwards. 33

34. Math 1140 - Financial Mathematics Quiz Monday Everything we covered up then except credit card interest. Monday Read sections 2.2, 2.3, 2.4 Wednesday Homework 4 is due. First Exam (max 15 points): 26 September 2011 at 7pm Location to be announced Charge 34