1. Lecture 18 Ordinary Annuities Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.edu/~ans5k/ Math 1140 Financial Mathematics

2. Math 1140 - Financial Mathematics Grade components CP is class participation. Maximum 165. HW is homework. Maximum 25. E1 is exam 1. Maximum 100. EC is extra credit and bonus questions. It includes the points for the bonus questions in homework 4, homework 5, and exam 1. Maximum 100. 2

3. Math 1140 - Financial Mathematics The exam was A)Too hard B)Hard C)Just about right D)Easy E)Too easy 3

4. Math 1140 - Financial Mathematics Problem 1 a from the study guide b similar to problem 1b in the exam sample c similar to problem 6 from practice problems Problem 2 a from the study guide and I wrote in HW 5 solutions I will give this on the exam until everybody gets it right b similar to problem 19 from practice problems 4

5. Math 1140 - Financial Mathematics Problem 3 similar to problem 4 in the sample exam Problem 4 similar to problem 3 in the sample exam Problem 5 a) similar to problem 20 in the practice problems b) problem 51 in the practice problems Problem 6 similar to problem 5 in the sample exam 5

6. Math 1140 - Financial Mathematics Problem 7 a) similar to problem 39 in the practice problems b) similar to problem 7 in the practice problems Problem 8 similar to problem 8 in the sample exam Problem 9 similar to problem 9 in the sample exam 6

7. Math 1140 - Financial Mathematics Do you feel your exam grade is a good reflection of your efforts in this class? A)Yes B)No C)I don’t know 7

8. Math 1140 - Financial Mathematics Exam 1 grade distribution 8

9. Math 1140 - Financial Mathematics Extra credit 9

10. Math 1140 - Financial Mathematics Questions About last class About homework 10

11. Math 1140 - Financial Mathematics Page 95, #12 How long it will take $1,000 to be worth $1,388 at 8%(2) if: a)You answer to the nearest (rounded) n? b)No interest is given and the worth is at least $1,388. c)We use simple interest (Banker’s rule) for a part of a period. 11

12. Math 1140 - Financial Mathematics Page 98, #18 A $10,000, 5-year note is sold in 1 year to a person requiring 7(4)%. Find the proceeds. 12

13. Math 1140 - Financial Mathematics Last time Review of compound interest. Solved some homework exercises. 13

14. Math 1140 - Financial Mathematics If a<b then a+b<a+c. If a bc. If a 0 then ac<bc. Show x 2 ≥ 0 Inequalities 14

15. Math 1140 - Financial Mathematics Suppose that you open an investment account with a deposit of $2000. A year later, you deposit another $2000. A year after that (two years after the account is opened), you deposit another $2000. If the investment pays an effective rate of 8%, how much is in the account immediately after the third deposit? Work on this together for 3- 4 minutes. 15

16. Math 1140 - Financial Mathematics 16

17. Math 1140 - Financial Mathematics Suppose that you open an investment account that pays an effective rate of 8%. If you make 40 annual deposits (each on January 1) of $1000 each, how much will be in the account immediately after the 40th deposit? A)40  $1,000 B)40  $1,000(1+0.08) C)$1,000(1+0.08) 39 + $1,000(1+0.08) 38 + $1,000(1+0.08) 37 +... + $1,000(1+0.08) 0 D)$1,000(1+39  0.08) + $1,000(1+38  0.08) + $1,000(1+37  0.08) +... + $1,000(1+0  0.08) 17

18. Math 1140 - Financial Mathematics Suppose that you open an investment account that pays an effective rate of 8%. If you make 40 annual deposits (each on January 1) of $1000 each, how much will be in the account immediately after the 40th deposit? The correct answer is C. If you answered A, then you forgot about the interest. You considered the interest rate to be zero. If you answered B, then you considered the interest for only one conversion period. 18

19. Math 1140 - Financial Mathematics How do we calculate: $1,000(1+0.08) 39 + $1,000(1+0.08) 38 + $1,000(1+0.08) 37 +... + $1,000(1+0.08) 0 ? 19 $1,000[(1+0.08) 39 + (1+0.08) 38 + (1+0.08) 37 +... + (1+0.08) 0 ] (1.08) 39 + (1.08) 38 + (1.08) 37 +... + (1.08) 0

20. Math 1140 - Financial Mathematics Geometric Series S = x n + x n-1 + … + x + 1 20

21. Math 1140 - Financial Mathematics Suppose that R dollars are deposited at equally spaced times in an account paying interest of i percent per time period, compounded once per period. If n such deposits are made, then immediately after the n th deposit the account balance S is 21

22. Math 1140 - Financial Mathematics Wednesday Homework 6 due Read sections 4.1 and 4.2 Project Teams due next Friday. Charge 22