1. Lecture 19 Ordinary Annuities Ana Nora Evans Sean Clark 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.edu/~ans5k/ Math 1140 Financial Mathematics

2. Math 1140 - Financial Mathematics Turn in your homework NOW! 2

3. Math 1140 - Financial Mathematics A)I am here and ready to go. B)I am here, but I’ll take a nap. C)I’m not here. D)What about them Lions, 4 - 0!!! E)Colts suck without Manning. 3

4. Math 1140 - Financial Mathematics Last time Answered many questions about the grading. For more info check the class website: http://www.cs.virginia.edu/~evans/finmath/2011/grading-details Solved some homework exercises. We learned about geometric series. 4

5. Math 1140 - Financial Mathematics Geometric Series S = x n + x n-1 + … + x + 1 xS – S = x n+1 + x n + … + x 2 + x – (x n + x n-1 + … + x + 1) xS – S = x n+1 - 1 5

6. Math 1140 - Financial Mathematics 1+3+3 2 +…+3 9 = A)(3 9 -3)/(3-1) B)(3 9 -1)/(3-1) C)(3 10 -3)/(3-1) D)(3 10 -1)/(3-1) E)3 9 -1 The correct answer is D. 6

7. Math 1140 - Financial Mathematics 3 2 +…+3 9 = A)(3 9 -3)/(3-1) B)(3 9 -1)/(3-1) C)3 2 (3 8 -3)/(3-1) D)3 2 (3 9 -3)/(3-1) E)3 2 (3 7 -3)/(3-1) 3 2 +…+3 9 = 3 2 (1+…+3 7 ) =3 2 (3 8 -3)/(3-1) 7

8. 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 8

9. Math 1140 - Financial Mathematics Suppose that a professional wrestler makes 9 annual deposits of $5,000 into an account paying an effective rate of 8.6%. How much is in the account immediately after the last deposit is made? Work in groups 3-4 minutes. 9

10. Math 1140 - Financial Mathematics Suppose that a professional wrestler makes 9 annual deposits of $5,000 into an account paying an effective rate of 8.6%. How much is in the account 23 years after the last deposit is made? Work in groups 3-4 minutes. 10

11. Math 1140 - Financial Mathematics Jane plans to save up for a car by making equal monthly deposits into a savings account for three years. If the account pays a nominal rate of 5.2% convertible monthly and her goal is to have $20,000 immediately after the last deposit, how large must her deposits be? Work in groups 5-6 minutes. 11

12. Math 1140 - Financial Mathematics 12

13. Math 1140 - Financial Mathematics Wednesday Homework 6 due Read sections 4.3 and 4.4 Project Teams due next Friday. Charge 13