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# ct010s11 - UNSW ACTL1001 Actuarial Studies and Commerce...

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UNSW ACTL1001 Actuarial Studies and Commerce Sample Solutions Exercises 11 Exercise 1 The unearned premium provision at the end of the financial year 31 December will be Quarter Premiums received Unearned Premium March 60,700 1 8 × 60700 = 7587 . 5 June 300,100 3 8 × 300100 = 112537 . 5 September 50,670 5 8 × 50670 = 31668 . 75 December 120,980 7 8 × 120980 = 105857 . 5 giving an unearned premium provision of \$ 257,651.25. Exercise 2 Profit is Premiums + Investment Income - Claims -Expenses- Increase in Policy Liability where Policy liability = unearned premium provision + outstanding claims provision so that Policy liability XX-1 = 5,090.4 Policy liability XX = 5 , 500 . 3 and profit equals 2 , 829 . 8 + 148 . 5 - 1 , 784 . 2 - 1 , 818 . 3 - (5 , 500 . 3 - 5090 . 4) = - 1 , 034 . 1 (a loss). We also have Earned premium = 2,829.8+1,038.9- 1 , 069 . 4 = 2 , 799 . 3 and Incurred Claims = 1,784.2+4,430.9-4,051.5 = 2 , 163 . 6 Now profit also equals Earned remiums + Investment Income - Incurred Claims -Expenses 1

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2 , 799 . 3 + 148 . 5 - 2 , 163 . 6 - 1 , 818 . 3 = - 1 , 034 . 1 (a loss) The expense ratio is expenses earned premium = 1 , 818 . 3 2 , 799 . 3 = 0 . 65 or 65% and the loss ratio is incurred claims earned premiums = 2 , 163 . 6 2 , 799 . 3 = 0 . 77
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