1. Lecture 20 Ordinary Annuities Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.edu/~ans5k/ Math 1140 Financial Mathematics

2. Math 1140 - Financial Mathematics Project Teams Please turn in a piece of paper with the names of your team members. If you do not have yet a team, write your name and what type of projects you would be interested in. 2

3. Math 1140 - Financial Mathematics My project team has A)1 member B)2 members C)3 members D)4 members E)more than four members 3

4. Math 1140 - Financial Mathematics Last time Worked on problems using the geometric series formula: 4

5. 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 5

6. Math 1140 - Financial Mathematics 6

7. An annuity is a sequence of payments, usually equal, received at equal intervals of time. The equal intervals are called payment intervals or rent period. The periodic rent is the periodic payment. The term of an annuity runs from the beginning of the first rent period to the end of the last rent period. 7

8. Math 1140 - Financial Mathematics An ordinary annuity is an annuity with payments at the end of each rent period. 8

9. Math 1140 - Financial Mathematics We calculated the future value of a number of equally spaced payments. What about the present value? 9

10. 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. The deposit is made at the end of the period. If n such deposits are made, then what is the value of the account at the time of the beginning of the first payment period? The present value of the first payment is R(1+i) -1. The present value of the second payment is R(1+i) -2 The present value of the third payment is R(1+i) -3 ….. The present value of the last payment is R(1+i) -n. 10

11. Math 1140 - Financial Mathematics P=R(1+i) -1 + R(1+i) -2 +…..+ R(1+i) -n P=R[(1+i) -1 + (1+i) -2 +…..+ (1+i) -n ] P=R(1+i) -n [(1+i) n-1 + (1+i) n-2 +…+ 1] 11

12. Math 1140 - Financial Mathematics Notations 12

13. Math 1140 - Financial Mathematics The present value of an annuity is also called the price of the annuity. Suppose that an annuity makes a sequence of 20 annual payments, the first coming a year from now. If each payment is $4000 and the effective rate is 9%, what is the price of the annuity? Price of annuity 13

14. Math 1140 - Financial Mathematics Questions? 14

15. Math 1140 - Financial Mathematics Homework If you finish the examples before the time is up, please work on your homework (for this class). 15

16. Math 1140 - Financial Mathematics CarMax advertises a vehicle for $2,000 down and $400 per month for two years financed at 10.5%(12). What is the cash price for this vehicle? 16

17. Math 1140 - Financial Mathematics Suppose that you take out a mortgage to buy a house. You borrow $210,000, and agree to repay the loan with monthly payments for 30 years, the first coming a month from now. If the interest rate is 6.25% convertible semiannually, what is the monthly payment? 17

18. Math 1140 - Financial Mathematics You've just purchased a 2002 Volkswagen Beetle GRS, and are financing the entire purchase price of $17,888. You bought the car on June 20, and tell the lender that you want your loan payments to be due on the 4 th of each month. If the interest rate is 10.2% convertible monthly, and you have a 60-month loan, how much is your monthly payment? Use simple interest and the effective interest rate for a part of a period. 18

19. Math 1140 - Financial Mathematics Monday No class Friday Homework 7 Due Project description due Charge 19