1. Math 1140 Financial Mathematics Lecture 4 More Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.edu/~ans5k/

2. Math 1140 - Financial Mathematics Homework 2 Turn in homework 2 now! I mean it! I will not accept it later! 2

3. Math 1140 - Financial Mathematics Questions? 3

4. Math 1140 - Financial Mathematics Homework 2 If a cycle contains a single charge denoted by C made on the first day of the cycle then the average daily balance and daily accrual give the same interest. Average Daily Balance: ADB = C * 30 / 30 = C Interest = ADB * cycle length * APR/365 = C * 30 * APR/365 Daily Balance: DB = C Interest per day = C * APR/365 Interest = 30 * C * APR/365 4

5. Math 1140 - Financial Mathematics Homework 2 If a cycle contains a single charge denoted by C made on the last day of the cycle then the average daily balance and daily accrual give the same interest. Average Daily Balance: ADB = C / 30 Interest = ADB * cycle length * APR/365 = (C /30) * 30 * APR/365 = C * APR/365 Daily Balance: DB = 0 for all the days except last, which is C Interest for the last day = C * APR/365 Interest = C * APR/365 5

6. Math 1140 - Financial Mathematics Homework 2 If a cycle contains a single charge then the average daily balance and daily accrual give the same interest. 6

7. Math 1140 - Financial Mathematics Trust your intuition, but verify Your intuition says it is better to pay a smaller interest rate. The difference in interest paid with average daily balance and daily accrual is pennies on the dollar. (assuming the same interest rate) The interest rates in the two methods differ by a factor of 2. 7

8. Math 1140 - Financial Mathematics Do not confuse average daily balance with two-cycle average daily balance. 8

9. Math 1140 - Financial Mathematics 9

10. Terms from last time Exact time Approximate time Ordinary interest Exact interest Banker’s Rule 10

11. Math 1140 - Financial Mathematics More practice Next homework! The odd number exercises from the textbook! 11

12. Math 1140 - Financial Mathematics Add-on Loan You purchase for $2,150 a 2000 Chevy Cavalier from friendly local dealer Defective Motors. He will finance your loan for two years, charging you 11% add-on interest on the loan. How much is your monthly payment? 12

13. Math 1140 - Financial Mathematics Solution Step 1 – calculate the maturity value of the loan Step 2 – calculate the monthly payments 13

14. Math 1140 - Financial Mathematics Thinking Time Is this the same as a simple interest loan? A)Yes B)No C)Maybe D)I was napping for the last 10 minutes or more This is a participation question. 14

15. Math 1140 - Financial Mathematics Discussion 15

16. Math 1140 - Financial Mathematics Even more thinking The value of the money I pay for a six months add-on loan compared with a simple interest loan paid at maturity is: A)Bigger B)Smaller C)Exactly the same D)I would like to go back to sleep This is a participation question. 16

17. Math 1140 - Financial Mathematics Discussion 17

18. Math 1140 - Financial Mathematics It’s legal! This type of financing is offered in in-store loans from appliance, furniture, and auto dealers. 18

19. Math 1140 - Financial Mathematics Break 19

20. Math 1140 - Financial Mathematics Prompt Payment Discount Discount offered for quick cash payments. Example: some medical bills, building constructors bills. Notation: 2/10 n/45 If the balance is paid in 10 days then there is a 2% discount. The full balance (net) is due in 45 days. 20

21. Math 1140 - Financial Mathematics Example Nora has to pay a $4,500 bill to her dentist. If she pays cash on the day of the service she gets a 5% discount. The full payment is due in 30 days. Assume she keeps the money in a savings account offering 2% simple interest rate. When should she pay? 21

22. Math 1140 - Financial Mathematics Prompt Payment 22

23. Math 1140 - Financial Mathematics Payment at the Deadline 23

24. Math 1140 - Financial Mathematics Which method is better? What interest rate would make it at least as good to pay later? 24

25. Math 1140 - Financial Mathematics 25

26. Math 1140 - Financial Mathematics Real life may be more complicated Dental insurance! 26

27. Math 1140 - Financial Mathematics Next time Partial Payments Start Discount Interest 27

28. Math 1140 - Financial Mathematics Charge Due Friday: Read sections 1.8, 1.9 Due Next Wednesday : Third homework 28