# 2007_q1s - ACTL 1001 Actuarial Studies and Commerce Class...

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Unformatted text preview: ACTL 1001 Actuarial Studies and Commerce Class Test 1 Tuesday, 28th August 2007 Sample Solutions 1. [8 marks] Assume that the probability that the number of hailstorms occurring in a year has a Poisson distribution with = 0 . 2 . What is the probability that in a 50 year period there will be at least 2 years with a hailstorm? Probability of a hailstorm in any year is . 2 e- . 2 = 0 . 16374615 Probability of at least 2 years with a hailstorm in 50 year period is 1- (1- . 1637) 50- 50 (0 . 1637) (1- . 1637) 49 = 0 . 9986 2. [14 marks] Given that the interest rate if 8%p.a. (compounded semi-annually) , calculate the following: a. [4 marks] effective annual rate b. [5 marks] the equivalent annual rate of interest, payable monthly c. [5 marks] the value of an 5 year annuity-due with payments of \$ 3 per annum. (a) j = 1 + . 08 2 2- 1 = 0 . 0816 (b) 1 + j (12) 12 12 = 1 + . 08 2 2 j (12) = 0 . 078698362 hence 7.8699% p.a (monthly compounding) (c) 3 .....
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## This note was uploaded on 08/23/2010 for the course ACTL 1001 taught by Professor Bernartwong during the Three '10 term at University of New South Wales.

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2007_q1s - ACTL 1001 Actuarial Studies and Commerce Class...

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