ETC2430 Exam Sem1 2019 final with all solutions - corrected PDF

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Warning: TT: undefined function: 32 Warning: TT: undefined function: 32 Warning: TT: undefined function: 32 Office Use OnlySemester One 2019Examination PeriodFaculty of Business and EconomicsEXAM CODES: ETCTITLE OF PAPER: ACTUARIAL STATISTICS – PAPER 1 OF 1EXAM DURATION: 2 hours writing timeREADING ...

Description

Office Use Only

Semester One 2019 Examination Period Faculty of Business and Economics EXAM CODES:

ETC2430

TITLE OF PAPER:

ACTUARIAL STATISTICS – PAPER 1 OF 1

EXAM DURATION:

2 hours writing time

READING TIME:

10 minutes

THIS PAPER IS FOR STUDENTS STUDYING AT: (tick where applicable)  Caulfield ✓ Clayton ✓Malaysia  Off Campus Learning  Parkville  Gippsland  Peninsula  Monash Extension  Other (specify)

 Open Learning  Sth Africa

During an exam, you must not have in your possession any item/material that has not been authorised for your exam. This includes books, notes, paper, electronic device/s, mobile phone, smart watch/device, calculator, pencil case, or writing on any part of your body. Any authorised items are listed below. Items/materials on your desk, chair, in your clothing or otherwise on your person will be deemed to be in your possession. No examination materials are to be removed from the room. This includes retaining, copying, memorising or noting down content of exam material for personal use or to share with any other person by any means following your exam. Failure to comply with the above instructions, or attempting to cheat or cheating in an exam is a discipline offence under Part 7 of the Monash University (Council) Regulations.

AUTHORISED MATERIALS OPEN BOOK

NO

CALCULATORS

NO

SPECIFICALLY PERMITTED ITEMS if yes, items permitted are:

NO

Candidates must complete this section if required to write answers within this paper

STUDENT ID:

__ __ __ __ __ __ __ __

DESK NUMBER:

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Page 1 of 12

INSTRUCTIONS TO CANDIDATES:

Answer ALL questions in this examination paper. Paper is out of 90 marks

Where you are asked to perform calculations, you should write out the solution as an equation containing the appropriate numerical values from within the question. You do not need to calculate exact values in order to receive full marks for that part of the question.

Question 1 (20 marks) Your company has launched a new insurance product and is projecting the premium cashflows, for budgeting purposes. You expect to steadily acquire new clients over the first year at a constant rate, and are projecting having 1,000 clients by the end of the year. Each client pays an annual premium of $10 in the first year. Define 𝑀(𝑡) as the total premium paid between time 0 and time 𝑡. 0.25

a. What does the expression ∫0 this definition of 𝑀(𝑡).

𝑀′ (𝑡)𝑑𝑡 represent? Evaluate the value of this integral with (5 marks)

This is the total amount of premium received in the first 3 months since launching this product. (2 marks) 𝑀(𝑡) = 10,000𝑡, so 𝑀′ (𝑡) = 10,000. ∫ (3 marks)

0.25

0

10,000𝑑𝑡 = [10,000𝑡]00.25 = $2,500 − $0 = $2,500

b. The company expects slower growth in clients in Years 2 and 3, with 500 new clients in Year 2, and 200 new clients in Year 3. They also expect some lapses, whereby 10% of those who paid the premium in Year 1 do not make the second year of payments, and 10% of those who paid the premium in Year 2 do not make payments in Year 3. Premiums will remain fixed at $10 per year for the three year period. i. Derive the expression(s) for 𝑀(𝑡) for the period 𝑡 = 0 through to 𝑡 = 3.

(8 marks)

M(t) = 10,000t, 0...