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

2. Math 1140 - Financial Mathematics Why do you take financial math? 2

3. Math 1140 - Financial Mathematics Easy A ? 3 Homework Class Participation Project Two Exams Final

4. Math 1140 - Financial Mathematics Project Ideas Federal Reserve System Explain the causes of a financial crisis – Bank panic of 1907 – Savings and loans crisis – 2008 financial crisis Analyze different options for a short term loan Explain the terms used in a “Mad Money” show Analyze a publicly traded company Build a stock portfolio 4

5. Math 1140 - Financial Mathematics Satisfy math requirement 5

6. Math 1140 - Financial Mathematics Become a financial guru 6

7. Math 1140 - Financial Mathematics Learn how to manage your finances 7 COMM 2730 - Personal Finance

8. Math 1140 - Financial Mathematics If you like this class, you may also like… MATH 5140 - Mathematics of Derivative Securities 8 Beware of prerequisites

9. Math 1140 - Financial Mathematics Learn about… How to calculate credit card interest How to calculate loan interest Annuities Stock investing Bonds More precisely, most of chapters 1-7 from the textbook. 9

10. Math 1140 - Financial Mathematics Additional Topics Email me! 10

11. Math 1140 - Financial Mathematics Do you own a credit card? A Yes B No 11

12. Math 1140 - Financial Mathematics What is interest? Interest is the fee paid by the borrower to the owner. 12 Interest rate is the percentage of the amount borrowed charged to the borrower for a fixed amount of time.

13. Math 1140 - Financial Mathematics APR What is APR? 13 Annual Percentage Rate How do you calculate the interest rate per day?

14. Math 1140 - Financial Mathematics When do you think are you charged interest for a credit card? A)Every month, even if you pay the bill on time B)When you don’t pay the entire bill C)Only when you don’t pay the minimum payment D)None of the above 14

15. Math 1140 - Financial Mathematics What is the amount you pay interest for? A)Only the amount from previous cycle B)The transaction from the previous and current cycle 15

16. Math 1140 - Financial Mathematics Methods for Calculating Credit Card Interest Average daily balance Adjusted balance Previous balance Two-cycle average daily balance Daily accrual 16

17. Math 1140 - Financial Mathematics Daily Accrual The interest is calculated daily, and billed at the end of each cycle. 17 I = sum of daily interest daily interest = daily balance * APR / 365

18. Math 1140 - Financial Mathematics Example Previous Balance: $2,500 Expenses and credits: Day 1: $200 Day 10: $1,000 Day 20: -$1,000 Day 25: $500 APR: 13.24% Cycle length: 30 days 18

19. Math 1140 - Financial Mathematics Daily Accrual In our example: Days 1-9: daily interest= $2,700 * 0.1324 / 365 = $0.97 Days 10-19: daily interest= $3,700 * 0.1324 / 365 = $1.34 Days 20-24: daily interest= $2,700 * 0.1324 / 365 = $0.97 Days 25-30: daily interest= $3,200 * 0.1324 / 365 = $1.16 I = 9 * $0.97 + 10 * $1.34 + 5 * $0.97 + 6 * $1.16 = $33.94 19

20. Math 1140 - Financial Mathematics Average Daily Balance First we calculate the average daily balance. add up the balance for each day and divide by the number of days Calculate the interest per day multiply the average daily balance with the daily interest rate Calculate the interest multiply the daily interest by the number of days 20

21. Math 1140 - Financial Mathematics Average Daily Balance I = ADB x APR x days in the billing cycle / 365 where I is the interest ADB is the sum of the balance of each day in the cycle divided by the number of days in the cycle. APR interest rate per year 21

22. Math 1140 - Financial Mathematics Average Daily Balance As a mathematical formula: where n is the number of days in the cycle B i is the balance on the i th day of the cycle * ADB is my notation 22

23. Math 1140 - Financial Mathematics Example I = ADB x APR x days in the billing cycle / 365 In our case: ADB = $3,133.33 APR = 13.24% days in the billing cycle = 30 I = $3,133.33 * 0.1324 * 30 / 365 = $34.09 23

24. Math 1140 - Financial Mathematics Adjusted Balance I = (previous balance – payments) x APR x days in the billing cycle / 365 In our example: previous balance = $2,500 payments = $1,000 I = ($2,500 - $1,000) * 0.1324 * 30 / 365 = $16.32 24

25. Math 1140 - Financial Mathematics Previous Balance I = previous balance x APR x days in the billing cycle / 365 In our example: previous balance = $2,500 I = $2,500 * 0.1324 * 30 / 365 = $27.20 25

26. Math 1140 - Financial Mathematics Two-cycle Average Daily Balance I = ADB x APR x days in the billing cycle / 365 where I is the interest ADB is the sum of the balance of each day in the current and previous cycle divided by the number of days in the two cycles. APR interest rate per year 26

27. Math 1140 - Financial Mathematics Question What do you think about the two-cycle average daily balance method of calculating interest? 27

28. Math 1140 - Financial Mathematics Office Hours In 403 Kerchof Hall Monday 1:00 – 2:30 Tuesday 3:30 – 5:00 By appointment Email me if you have conflicts with both times Feel free to stop by my office, but I might not be there… 28

29. Math 1140 - Financial Mathematics Office Hours What to do before coming to office hours Read your class notes Try to solve the homework by yourself 29 I will ask for help. I will make a reasonable effort to do things on my own first, but will ask my classmates or the course staff for help before getting overly frustrated.

30. Math 1140 - Financial Mathematics Office Hours Don’t Do not hang out in my office Do not do your homework in my office. Do not come in my office if you are stopping by unannounced and there is a ‘Do not disturb’ notice on my door. 30

31. Math 1140 - Financial Mathematics Charge Due Friday: Read sections 1.2 and 1.3 and Syllabus First homework Signed course pledge Registration Survey Due Next Wednesday (31 August): Second homework 31