INTRODUCTION TO INTERTEMPORAL ANALYSIS Friday, October 20

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INTRODUCTION TO INTERTEMPORAL ANALYSISFriday,
October 20
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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

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Compounding

• The Formula
• FV PV(1g)T
• Initial value / present value PV
• Final value / future value FV
• Average growth rate or interest per period g
• Number of time periods T

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Future Value Example

• 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?
• A. The initial value is 751, the growth rate is
  2.5 (.0251), and the time horizon is 35 years.

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Average Growth Rate Example

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

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Present Value Example

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

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An Introduction to the Mathematics of Finance

• Q What is a Bond?
• A A promise to pay in the future
• Q What is the price of a Bond?
• A How much you need to pay today to buy the
  future payment(s)?
• Q What does the bonds price depend on?
• A How fast money grows

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Determining the Price of a Bond

• The Deal
• On January 1 you are offered the following deal
  100 on January 1 for the next three years
• The Starting Point
• A dollar a year from now is not worth a dollar
  today so we must convert the future dollars to
  present dollars.

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The Framework

• Compounding formula provides framework
• PV 100/(1r) 100/(1r)2 100/(1r) 2
• r expected interest rate (growth rate of money)

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The Key to Intertemporal Analysis

• The Compounding Formula
• FV PV(1g)T