2. INTRODUCTION TO INTERTEMPORAL ANALYSIS Friday, October 20

3. Common Measures of Change Change = (FV-PV) (1,177.6 - 984.7) = 192.9 Percentage Change = (FV-PV)/PV =(1,177.6 - 984.7)/984.7 =.195 = 19.6%

4. Compounding F F The Formula FV = PV*(1+g) T F F Initial value / present value = PV F F Final value / future value = FV F F Average growth rate or interest per period = g F F Number of time periods = T

5. Future Value Future Value Example u u Q. What will the population of India be in the year 2020 if the population in 1985 was 751 million and the growth rate is 2.5% a year? u u A. The initial value is 751, the growth rate is 2.5% (.0251), and the time horizon is 35 years.

6. Average Growth Rate Average Growth Rate Example u u Q.What was average yearly rate of wage growth if wages grew from $102 in 1970 to $389 in 1989? u u A. The present value is 102, the future value is 389, and the time period is 19.

7. Present Value Present Value Example u u Q. How much will I need to save today to have $1,000 in 3 years if the interest rate is 8%.? u u A. The end value is $1,000, the time horizon is 3 years, and the growth rate is 8%..

8. An Introduction to the Mathematics of Finance u u Q: What is a Bond? u u A: A promise to pay in the future u u Q: What is the price of a Bond? u u A: How much you need to pay today to ‘buy’ the future payment(s)? u u Q: What does the bond’s price depend on? u u A: How fast money grows

9. Determining the Price of a Bond The Deal: u u On January 1 you are offered the following deal: $100 on January 1 for the next three years The Starting Point: u u A dollar a year from now is not worth a dollar today so we must convert the ‘future’ dollars to ‘‘present’ dollars.

10. The Framework: u u Compounding formula provides framework: PV = 100/(1+r) + 100/(1+r) 2 + 100/(1+r) 2 r = expected interest rate (growth rate of money)

11. The Key to Intertemporal Analysis The Compounding Formula FV = PV*(1+g) T