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W10-11Tute 1001 - Examples Doug is 18 years old and buys an...

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Examples Doug is 18 years old and buys an insurance policy that pays $100 if he dies in the first year, $200 if he dies in the second year, $150 if he dies in the third year, and $200 if he survives to the end of the three years. Payments are made at the end of the year of death/survival. Premiums are paid annual in advance. The insurer pays initial expenses of $10, as well as premium expenses of $5 + 2% of each premium received. The interest rate is 6% p.a. and p 18 = 0 . 7 , p 19 = 0 . 6 , p 20 = 0 . 5 , p 21 = 0 . 4 1. Explain why Doug’s benefits can be expressed as 50 A 18 : 1 3 | {z } 8 . 8160 + 150 A 18 : 3 | {z } 132 . 7287 + 50 A 1 18 : 2 | {z } 26 . 6109 - 100 A 1 18 : 1 | {z } 28 . 3019 = 139 . 8537 2. Show that the fair premium is P = 80 . 2735 . 3. Show that the reserves for this policy are 1 V = 53 . 5544 , 2 V = 91 . 4263 , 3 V = 200. Hint: ( t V + P - Exp t )(1+ i ) = ( q x + t )Ben t +1 +( p x + t ) t +1 V UNSW Week 10 ACTL1001 Tutorial
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Examples Benefits Draw a diagram! 150 A 18 : 3 represents receiving $150 at the end of the year of death for the next 3 years, or survival for the next 3 years. Since Doug should receive $200 in total on survival, we need to add 50 A 18 : 1 3 . Similarly, since he receives $200 if he dies during
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