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# ct010s06 - UNSW ACTL1001 Actuarial Studies and Commerce...

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UNSW ACTL1001 Actuarial Studies and Commerce Solutions Tutorial Exercises 6 Exercise 1 Now the payments are monthly, so we need a per month interest rate. The interest rate is 5% p.a. quarterly so the monthly rate is i where (1 + i ) 3 = 1 + 0 . 05 4 or i = 1 + 0 . 05 4 1 3 - 1 = 0 . 0041494 Present value is 1000¨ a 60 at rate 0 . 0041494 = 1000 (1 . 0041494) 1 - ( 1 1 . 0041494 ) 60 0 . 0041494 = 1000 × 53 . 23732 = 53 , 237 . 32 Exercise 2 Present value is 100 , 000 v 5 at 6% = 100 , 000 × 1 (1 . 06) 5 = 74 , 725 . 82 Exercise 3 Note: For Parts 1-3, one very important concept you will need to understand is how to setup a table (eg in a spreadsheet format) listing the cashflows, interest, PL and Asset values, and in particular the recur- sive/formula links between each item on the table. Please also find attached a spreadsheet which demonstrates these relationships. You should ensure that you can replicate this by hand as that is a great way of learning how each item (eg premiums, claims, expenses, PL, interest etc) relate to each other at a particular period and also between periods). 1

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1. Premium will be given by (using the principle of equivalence) P ¨ a 5 = 100 , 000 v 5 + 8 , 000 + 0 . 02 P ¨ a n + 100¨ a 5 at 6% so that P = 1 (1 - 0 . 02) " 100 , 000 v 5 ¨ a 5 + 8 , 000
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