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Tutorial 7

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

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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

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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 at which the bond was bought. No tax is payable on the coupons. What price should the purchaser pay to realize an annual effective yield of 4% after taxes?
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Tutorial 7 - 07/08 Semester II THE UNIVERSITY OF HONG KONG...

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