introduction to intertemporal analysis friday, october 20

INTRODUCTION TO INTERTEMPORAL ANALYSIS

Friday, October 20

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%

Compounding

The Formula FV = PV*(1+g)T

Initial value / present value = PV Final value / future value = FV Average growth rate or interest

per period = g Number of time periods = T

Future ValueFuture 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.

Average Growth RateAverage 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.

Present ValuePresent 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%..

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 bond’s price

depend on? A: How fast money grows

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.

The Framework:

Compounding formula provides framework:

PV = 100/(1+r) + 100/(1+r)2 + 100/(1+r) 2

r = expected interest rate (growth rate of money)

The Key to Intertemporal Analysis

The Compounding Formula FV = PV*(1+g)T