1. Lecture 2 Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.edu/~ans5k/ Math 1140 Financial Mathematics

2. Math 1140 - Financial Mathematics First Homework 2 Turn it in now!!! No late homework is accepted, unless you asked for an extension before and I agreed.

3. Math 1140 - Financial Mathematics Questions 3 Syllabus Last class

4. Math 1140 - Financial Mathematics Class Participation Ask questions Answer questions Clickers 4

5. Math 1140 - Financial Mathematics Types of clicker questions Anonymous You get 2 points for answering. I don’t see your answer. Participation You get 2 points for answering. I will see your answer. Correct/Incorrect You get 2 points for an incorrect answer. You get 3 points for an correct answer. 5

6. Math 1140 - Financial Mathematics Are you awake? A)Yes B)No This is an anonymous question. 6

7. Math 1140 - Financial Mathematics Collab I put the participation grades in Collab. I gave maximum credit to everybody that participated in the first class. 7

8. Math 1140 - Financial Mathematics What do you think about the class? 8 A)I would like to drop the class, but I can’t B)I plan to drop the class C)I love the class and plan to stay D)I plan to take a nap during class E)I don’t care about anything This is an anonymous question.

9. Math 1140 - Financial Mathematics Last Time 9 We started to learn about credit cards. Interest Interest Rate Methods for calculating interests Daily Accrual Average Daily Balance

10. Math 1140 - Financial Mathematics What is interest? A)An amount of money you pay to borrow money B)A percentage C)A time interval D)The amount of money you borrow This is a correct/incorrect question. 10

11. Math 1140 - Financial Mathematics Today Brief review of the first lecture Talk about second homework Start Simple Interest 11

12. Math 1140 - Financial Mathematics Math is easy, life is messy 12 Flickr cc:bitzcelt

13. Math 1140 - Financial Mathematics What is interest? Interest is the fee paid by the borrower to the owner. 13 Interest rate is the percentage of the amount borrowed charged to the borrower for a fixed amount of time.

14. Math 1140 - Financial Mathematics Simple Interest I = Pit I = interest (Cost for the use of the borrowed money) P = principal (Amount of money borrowed) i = interest rate (Percent of the principal that is the basis for the interest for a given time period) t = term (Length of the loan in time units) 14

15. Math 1140 - Financial Mathematics Maturity Value S = P + I S = maturity value (future value, amount) The amount of money a borrower will pay back. 15

16. Math 1140 - Financial Mathematics What does this mean? Alice borrows from Bob $100 for one year with 14% per year interest. How much money does Alice pay in interest? 16 Bob gives Alice $100 today, 26 August 2011. On 26 August 2012, Alice gives back $100 plus the interest. The interest is 14% of $100.

17. Math 1140 - Financial Mathematics What is %? What does 14% mean? A)0.14 B)1.4 C)14 D)0.014 E)140 17

18. Math 1140 - Financial Mathematics What about 0.02%? A)2 B)0.02 C)0.0002 D)20 E)200 18

19. Math 1140 - Financial Mathematics From words to formula Alice borrows from Bob $100 for one year with 14% per year interest. How much money does Alice pay in interest? Given: principal: P = interest rate: i = term: t = Unknown (what we need to calculate): interest: I = 19

20. Math 1140 - Financial Mathematics What about days? Bob wants to earn 14% per year for its money. Alice wants $100 for one day. Given: principal: P = interest rate: i = term: t = Unknown (what we need to calculate): interest: I = 20

21. Math 1140 - Financial Mathematics Back to money Bob wants to earn 14% per year for its money. Alice wants $100 for one day. interest rate: i = interest: I = 21

22. Math 1140 - Financial Mathematics Were did we see this before? APR = annual percentage rate = a percentage, like 14% How do you calculate the interest rate per day? annual rate = per year interest rate = APR per year = APR / 365 per day 22

23. Math 1140 - Financial Mathematics We saw I = Pit last time 23 I = sum of daily interest daily interest = daily balance * APR / 365 I = ADB x APR x days in the billing cycle / 365

24. Math 1140 - Financial Mathematics Daily Accrual daily interest = daily balance * APR / 365 I = P = i = t = 24

25. Math 1140 - Financial Mathematics Average daily balance The interest is: ADB x APR x days in billing cycle / 365 I = P = i = t = 25

26. Math 1140 - Financial Mathematics Math is POWER You need to know one formula I = Pit And units of measurement conversion 1 year = 365 days Multiplication and division 26

27. Math 1140 - Financial Mathematics Life is complicated … Why makes the formulas look so different? 27 The principal! For daily accrual: P = day balance For average daily balance: P = average daily balance

28. Math 1140 - Financial Mathematics 28

29. Math 1140 - Financial Mathematics There is a bit more math here… “Average” Daily Balance?!!!!! 29

30. Math 1140 - Financial Mathematics Simple Interest Home equity loans Promissory notes Bonds 30

31. Math 1140 - Financial Mathematics What is missing? Mortgage Credit card loans 31 I only told you how to calculate interest for one billing cycle! At the end of the cycle the interest is added to the balance. Next cycle the borrower pays interest on interest!

32. Math 1140 - Financial Mathematics Compound interest We’ll talk about it in a few weeks. Assuming the same interest rate, for which type of interest the borrower pays more: A)Simple interest B)Compound interest This is a participation question. 32

33. Math 1140 - Financial Mathematics Simple vs Compound Interest Simple interest grows linearly. Compound interest grows exponentially. 33

34. Math 1140 - Financial Mathematics Second Homework First problem Understand what real credit cards do Second and third problems Easy applications of average daily balance method 34

35. Math 1140 - Financial Mathematics Last Problem We have not covered enough to solve it! If you know it already, take a golf class! But first tell me the answer. What I want you to do? Think! Use a search engine (Google, duckduckgo, Bing)! 35

36. Math 1140 - Financial Mathematics Last Problem Nora has a pressing $22,000 financial need. She can use one of the following methods to pay it: – Credit card loan with APR= 16.24% and using average daily balance method – Margin loan with 9% per year interest rate and using daily accrual interest (compounded monthly). – Sell stock. Assume a return on investment of 14.32%. She can pay back $3,000 monthly. Which method is the most advantageous for her to use to pay the $22,000? 36

37. Math 1140 - Financial Mathematics Suggestions Use a search engine to find interest calculators. Is one method obviously wrong? Think about capital gains tax. Is the return on investment realistic? What are the risks of owning stock? 37

38. Math 1140 - Financial Mathematics Another example Guido the Enforcer offers you a simple interest loan of $1,000 at 3% weekly rate. Is this a good deal or a bad one? A)Really good B)Good C)Bad D)Run as fast as you can This is a participation question. 38

39. Math 1140 - Financial Mathematics Lets calculate … Guido the Enforcer offers you a simple interest loan of $1,000 at 3% weekly rate. 39

40. Math 1140 - Financial Mathematics What is the interest per year? 40

41. Math 1140 - Financial Mathematics Other types of problems Given the interest, the interest rate and the term of a simple interest rate, what is the principal? 41

42. Math 1140 - Financial Mathematics Other types of problems What is the formula for interest rate? What is the formula for the term? 42

43. Math 1140 - Financial Mathematics Next time More about simple interest I will continue with section 1.3 43

44. Math 1140 - Financial Mathematics Charge Due Monday: Read sections 1.3 and 1.4 Due Next Wednesday (31 August): Second homework 44