Tutorial 7

Tutorial 7 - 07/08 Semester II THE UNIVERSITY OF HONG KONG...

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Unformatted text preview: 07/08 Semester II THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1802 Financial Mathematics Tutorial 7 1 Review 1.1 Basic Formula P = F · r · a n e i + C · v n 1.2 Premium/Dicount Formula P = F · r · a n e i + C (1- i · a n e i ) = C + ( F · r- C · i ) a n e i Premium = P- C = ( F · r- C · i ) a n e i = C ( g- i ) a n e i P > C, g > i Discount = C- P = ( C · i- F · r ) a n e i = C ( i- g ) a n e i P < C, g < i 1.3 Makeham’s Formula 1. No Income Tax P = K + g i ( C- K ) F · r = C · g C = X j C j , K = X j K j = X j C j v n j 1 P = X j C j v n j + X j C j · g · a n j e i 2. Incorporating Income Tax P = K + g (1- t 1 ) i ( C- K ) 3. Incorporating Income Tax and Capital Gains Tax P = K + g (1- t 1 ) i ( C- K )- t 2 ( C- P C ) K Capital gain: C j- F j F P ( g (1- t 1 ) < i ) Capital gains tax: k X j =1 t 2 ( C j- F j F P ) v n j 2 2 Exercises 1. A $500, 3% bond with annual coupons is redeemable at par in 8 years. When the bond matures, the bondholder is subject to a tax of 10% on the amount of discount...
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This note was uploaded on 04/17/2011 for the course STAT 1802 taught by Professor Dr.k.c.yuen during the Spring '08 term at HKU.

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Tutorial 7 - 07/08 Semester II THE UNIVERSITY OF HONG KONG...

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