Fin300.Lecture2.TVMnotes - Lecture 2:The Time Value of...

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Lecture 2:The Time Value of Money
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This lecture note covers: :: Simple Interest vs. Compound Interest :: :: Fundamental tools for financial analysis :: § Present Value and Future Value/ Discounting § Compounding Intervals § Continuous Compounding :: Useful Shortcuts :: § Annuities and Perpetuities § Growing annuities and perpetuities
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C n : Future value at end of n periods of C 0 dollars today C 1 = C 0 + rC 0 (deposit C 0 for 1 period) C 1 = C 0 (1 + r) C 2 = C 1 + rC 1 (deposit C 1 for 1 period) C 2 = C 1 (1 + r) = C 0 (1 + r) 2 Recursively C n = C 0 (1 + r) n Compound Interest Formula
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Example: $1000 at 5% for 5 years Year Beginning Amount Interest on Original Principle Interest on Interest Ending Amount 1 1000.00 50.00 0.00 1050.00 2 1050.00 50.00 2.50 1102.50 3 1102.50 50.00 5.13 1157.63 4 1157.63 50.00 7.88 1215.51 5 1215.51 50.00 10.78 1276.28 C 5 = 1000(1.05) 5 = 1000 × 1.2763 = 1276.28
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Simple vs. Compound Interest
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Present Values/Discounting C n = C 0 (1 + r) n FV n = PV 0 (1 + r) n PV 0 = FV n /(1 + r) n Present values are ADDITIVE PV(C 1 ,C 2 ,...,C n ) = PV 1 (C 1 ) + PV 2 (C 2 ) + ... + PV n (C n ) = t = 1 n PV t (C t )
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Example : "Claim X" : $100 a year at the end of each year for 10 years.
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