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Tone the Phone

Back to School 2017 Contest Question

Problem: Tone My Phone 

Actuarial work deals with events that

  1. May happen in the future, but
  2. Are uncertain, and
  3. Have a financial impact.

The following exercise is fictitious, but it highlights some of the skills actuaries need to use.

Here is the problem:

A renowned electronics outlet has retained your actuarial services to design protection plans for mobile phones (of course, cracked glass and physical damage are not covered). They tell you that in any given year, a typical device has a probability of failure of 5%. They also want to make a 10% profit on this protection plan. Based on this, you came up with the following proposed plan for a $500 device:

  • A reimbursement of $500 if the device fails during the first year; and
  • The amount of the reimbursement decreases by $100 each successive year until it reaches zero. 

If the price of this plan is based on the expected average reimbursement over the life of the plan, what should it be? You should account for the chance of the device failing in any given year of this insurance contract.

Once you have read these sections and calculated your answer, please send it to tonemyphone@cia-ica.ca by May 31, 2017.

We will draw a winner for an iPad Air 2 on June 1, 2017. One entry per person, please. This contest is open only to students currently enrolled at a Canadian secondary school.

Good luck!