1. Lecture 12 Compound Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.edu/~ans5k/ Math 1140 Financial Mathematics

2. Math 1140 - Financial Mathematics A)I finished homework 5. B)I didn’t start homework 5. C)I got stuck in a problem in homework 5. D)Do we have a homework!? If you answered C you should come to the office hours. 2

3. Math 1140 - Financial Mathematics Office Hours Monday 11:00-12:30 Tuesday 3:30-5:00 Friday 2:30-3:30 In Ker 403. 3

4. Math 1140 - Financial Mathematics Review Session It is not required. It will be useful for students that joined the class late and missed the first few classes. It offers the chance to clarify some concepts from the previous classes. 4

5. Math 1140 - Financial Mathematics I am sorry for Sunday. Is Wednesday 7pm working for you? A)It works and I plan to come. B)I can come to office hours instead. C)I would like to come but I have other commitments. D)I don’t need extra help. If you answered C please email me to make an appointment or come prepared to ask questions on Friday and Monday. Review Session 5

6. Math 1140 - Financial Mathematics Questions About last class About homework 6

7. Math 1140 - Financial Mathematics Sample exam 1 posted Practice exercises posted (we will work on them in class on Friday, Sep 23, and Monday, Sep 26). Exam 1 covers sections 1.2 trough 1.9 sections 2.1 trough 2.5 sections 3.1 and 3.2 7

8. Math 1140 - Financial Mathematics Plan for this week Monday(today) – sections 3.4 and 3.5 Wednesday – sections 3.6 and 3.7 Friday and Monday(exam review, work in groups on practice problems, class in Rice Hall first floor) 8

9. Math 1140 - Financial Mathematics Last time Started compound interest. Compound amount formula Present value at compound interest Sections 3.1 and 3.2 9

10. Math 1140 - Financial Mathematics Today Annual effective rate Annual effective rate of compound discount Compound rate formula Sections 3.4 and 3.5 10

11. Math 1140 - Financial Mathematics m is the number of conversion periods per year. i(m) is the nominal interest rate. Interest rate per conversion period i = i(m)/m Nominal Interest Rate and Interest Rate 11

12. Math 1140 - Financial Mathematics Compound amount formula is S = P(1+i) n where n is the total number of conversion periods P is the principal S is the amount i is the interest rate per conversion period Present value formula at compound interest is P = S(1+i) -n 12

13. Math 1140 - Financial Mathematics Obsetvation n, the total number of conversion periods is a natural number. For any fractions of a conversion period, use simple interest formula. E.g., after calculations you end up with 3.5 conversion periods then the amount is S = (P(1+i) 3 )(1 + 0.5 x i) 13

14. Math 1140 - Financial Mathematics Questions? 14

15. Math 1140 - Financial Mathematics Suppose that a savings account pays 3% interest per quarter compounded quarterly. If $2,500 is deposited, how much is in the account 5 years later? A) 2,500(1+0.03/4) -5 B) 2,500(1+0.03) -20 C) 2,500(1+0.03/4) 5 D) 2,500(1+0.03) 20 E) I don’t know Pledged Question 15

16. Math 1140 - Financial Mathematics Suppose that a savings account pays 3% interest per quarter compounded quarterly. If $2,500 is deposited, how much is in the account 5 years later? Answer 16 The interest rate is given as interest rate per conversion period, thus i = 3%. Since there are 4 conversion periods per year and the term is 5 years, then n = 20. The principal is P=$2,500. The correct answer is 2,500(1+0.03) 20

17. Math 1140 - Financial Mathematics Google Group I created a google group for this class FinMathFall2011. You must join the group to receive class emails. The 13 students did not join are doing it at their own risk. One of the messages on the group list tells you how to subscribe for updates of the class website. 17

18. Math 1140 - Financial Mathematics Emails To receive my emails you must whitelist my email addresses: AnaNEvans@gmail.com AnaNEvans@virginia.edu ans5k@virginia.edu 18

19. Math 1140 - Financial Mathematics Warning From now on you are responsible for any emails sent to your UVa email address and to the FinMathFall2011 google group. 19

20. Math 1140 - Financial Mathematics Annual Effective Rate Given a nominal interest rate i(m), the annual effective rate is the interest rate i such that if the same principal P is deposited in two accounts: one with nominal interest rate i(m) and one with yearly interest rate i, compounded yearly; at the end of one year the two accounts have the same balance. 20

21. Math 1140 - Financial Mathematics The compounded amount formula is S = P(1+i) n The balance in an account with nominal interest rate i(m) after one year is: S = P(1 + i(m)/m) m The balance in an account with interest rate i per year, compounded yearly, after one year is S = P(1 + i) 1 To calculate i P(1 + i) = P(1 + i(m)/m) m i = (1 + i(m)/m) m - 1 21

22. Math 1140 - Financial Mathematics Why does one calculate annual effective rate? 22 It allows us to compare different nominal interest rates. You are considering two different savings accounts. The first pays 4.7% compounded monthly and the second one pays 4.63% compounded daily. Which one is the better deal?

23. Math 1140 - Financial Mathematics You are considering two different savings accounts. The first pays 4.7% compounded monthly and the second one pays 4.63% compounded daily. Which one is the better deal? The annual effective rate formula is 1+i = (1 + i(m)/m) m For the first account: For the second account: 23

24. Math 1140 - Financial Mathematics Wednesday Homework 5 due Read sections 3.4, 3.5, 3.6, 3.7 Friday and Monday Exam 1 review First Exam (max 15 points): 26 September 2011 at 7pm in CLK 108 Charge 24