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INTRODUCTION TO INTERTEMPORAL ANALYSIS
Friday, 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*(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
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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.
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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.
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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%..
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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 bond’s 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/(1+r) + 100/(1+r)2 + 100/(1+r) 2
r = expected interest rate (growth rate of money)
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The Key to Intertemporal Analysis
The Compounding Formula FV = PV*(1+g)T