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Unformatted text preview: Examples Tim is exactly 21 years old and purchases a pure endowment policy with term of 3 years, paying a lump sum of $ X if he survives to his 24th birthday. He pays premiums of $1000, $2000 and $5000 at the start of each year. The insurer pays 1%, 2% and 3% respectively of each of these premiums as expenses, in addition to initial expenses of $400, and fixed expenses of $100 on the receipt of each premium. The interest rate is assumed to be 4% p.a. effective for the next 3 years. Assume that 3 p 21 = 1. 1. Calculate $X with the principle of equivalence. 2. Let PL ( n ) denote the policy liability to the insurer at the end of the n th year. Show that PL (1) = $509 . 6 , PL (2) = $2464 . 384. 3. Determine the insurer’s profit in the 3rd year if the interest rate unexpectedly changes to 5% p.a. effective at the end of the 2nd year. UNSW Week 7 ACTL1001 Tutorial Examples Calculating the Lump Sum By the Principle of Equivalence, we have: APV (Premiums) = APV (Benefits + Expenses) Actuarial Present Value of Premiums: 1000 + 2000 1 . 04 + 5000 1 . 04 2 = 7545 . 857988 Actuarial Present Value of Benefits and Expenses:...
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This note was uploaded on 06/12/2011 for the course ASB 1001,2522, taught by Professor Nicole during the One '09 term at University of New South Wales.
 One '09
 Nicole

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