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Unformatted text preview: IMSE3010 Financial Engineering ecture 2 Lecture 2 FixedIncome Securities Miao Song Dept of Industrial & Manufacturing Systems Engineering eview of Lecture 1 Review of Lecture 1 Introduction to Financial Engineering What is Financial Engineering g g Present Value Synthetic Replication Effective Annual Rate Periodic Compounding Continuous Compounding FV = PV × (1 + r EAR ) t 1/18/2011 2 1/18/2011 2 genda Agenda Present Value Annuity and Perpetuity y p y Mortgage Calculation FixedIncome Securities 1/18/2011 3 1/18/2011 3 nnuity Annuity Today is t = 0 and cash flow starts at t = 1 A A A …… t = 0 t = 1 t = T time t = 2 T T A A A A Annuity PV 1 1 1 ) ( 2 T r Annuity PV Annuity FV r r r r r 1 ) ( ) ( 1 1 1 1 1/18/2011 4 1/18/2011 4 xample Example An insurance company sells an annuity of $10,000 per year for 20 years. Suppose r = 5%. What should the company sell it r? for? 05 . 1 1 1 05 . 1 000 , 10 ) ( 20 Annuity PV 1 . 622 , 124 46 . 12 000 , 10 1/18/2011 5 1/18/2011 5 erpetuity Perpetuity A perpetuity is an annuity with infinite maturity A A A …… t = 0 t = 1 t = 3 time t = 2 PV(Perpetuity) = A / r 1/18/2011 6 1/18/2011 6 xample Example You just won the lottery and it pays $100,000 a year for 20 years. Are you a millionaire? Suppose that r = 10%. 1 1 00 00 nnuity V 56 51 14 00 00 1 . 1 1 1 . 000 , 100 ) ( 20 Annuity PV 356 , 851 514 . 8 000 , 100 1/18/2011 7 1/18/2011 7 xample (cont ) Example (cont.) What if the payments last for 50 years? 1 . 1 1 1 1 . 1 000 , 100 ) ( 50 Annuity PV ow about forever? 481 , 991 915 . 9 000 , 100 How about forever? PV(Perpetuity) = 100,000 / 0.1 = 1M 1/18/2011 8 1/18/2011 8 ortgage Calculation in US Mortgage Calculation in US Pay 20% down payment, and borrow the rest from the bank using the property as collateral ay a fixed monthly payment for the life of Pay a fixed monthly payment for the life of the mortgage Have the option to prepay the mortgage nytime before the maturity of the anytime before the maturity of the mortgage 1/18/2011 9 1/18/2011 9 ortgage (cont ) Mortgage (cont.) Suppose that you bought a house for $500,000 with $100,000 down payment and financed the rest with a thirtyyear xed rate mortgage at 8 5% APR fixed rate mortgage at 8.5% APR compounded monthly What is the effective annual interest rate?...
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This note was uploaded on 12/09/2011 for the course IMSE 0301 taught by Professor Song during the Spring '11 term at HKU.
 Spring '11
 SONG

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