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IOE+201+Notes+5 - IOE 201 Lecture Notes 5 Compound Interest...

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1 Compound Interest: Different Interest Rates in Each Interest Period P = Present worth ($) i = Interest rate per period N = Number of periods F = Future ($) at end of N periods If interest rate i is same in each interest period, F = P (1 + i ) N If interest rate is different in each interest period, F = P (1 + i 1 )(1 + i 2 )(1 + i 3 ) …… (1 + i N ) where i 1 , i 2 , …… , i N are the interest rates in interest periods 1, 2, …… , N IOE 201 Lecture Notes 5
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2 0 1 2 3 Time Interest Periods P F Compound Interest: Different Interest Rates in Each Interest Period F = P (1 + 0.03)(1 + 0.05)(1 + 0.02) 3% 5% 2% Example: Interest Rates
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3 Inflation Inflation : Loss of purchasing power over time (cost of an item increases over time) Deflation (opposite of inflation): Gain in purchasing power over time (cost of an item decreases over time) Consider inflation : Denote inflation rate (% per year) by f Inflation rate f generally changes in each year
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4 Inflation If inflation rate is 5% in first year 7% in second year 4% in third year the cost of a $1 item increases to $1(1 + 0.05)(1 + 0.07)(1 + 0.4) = $1.17
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