Lecture 2

# Lecture 2 - IMSE3010 Financial Engineering ecture 2 Lecture...

This preview shows pages 1–11. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: IMSE3010 Financial Engineering ecture 2 Lecture 2 Fixed-Income 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  Fixed-Income 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 thirty-year xed rate mortgage at 8 5% APR fixed rate mortgage at 8.5% APR compounded monthly  What is the effective annual interest rate?...
View Full Document

## This note was uploaded on 12/09/2011 for the course IMSE 0301 taught by Professor Song during the Spring '11 term at HKU.

### Page1 / 39

Lecture 2 - IMSE3010 Financial Engineering ecture 2 Lecture...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online