# Actuarial Discussion Forum - Professional Discussions for Professional Actuaries

 D.W. Simpson & Co, Inc. - Worldwide Actuarial Jobs Life Jobs Health Jobs Pension Jobs Casualty Jobs Salary Apply Pauline Reimer, ASA, MAAA - Pryor Associates Nat'l/Int'l Actuarial Openings: Life P&C Health Pensions Finance ACTEX Publications and MadRiver Books Serving students worldwide for over 40 years Advertise Here - Reach Actuarial Professionals Advertising Information Actuarial Careers, Inc.® - Actuarial Jobs Worldwide Search positions by geographic region, specialization, or salary Ezra Penland Actuarial Recruiters - Top Actuarial Jobs Salary Surveys  Apply Online   Bios   Casualty   Health   Life   Pension

# Thread: Pro-rata Share of the Purchase Price

1. ## Pro-rata Share of the Purchase Price

An auto repair shop plans to sell a new brand of car battery with a 4-year warranty. Given:

(i) If the battery fails within 4 years, the shop will refund a pro-rata share of the purchase price at the moment of failure.
(ii) The purchase price of the battery is equal to the sum of the manufacturing cost, loading for profit, and the actuarial present value of the warranty.
(iii) The manufacturing cost of the battery is 50, and profit is equal to 10% of the manufacturing cost.
(iv) The force of failure of the battery is mu(t) = 1/(10-t), 0 <= t < 10.
(v) delta (d) = 0.05

Calculate the purchase price of the battery. The answer is 67.68. I calculated to be E(Z) = 0.217732*P , which I think is correct, but I don't get where the manufacturing cost fits in? Thanks.

There are currently 1 users browsing this thread. (0 members and 1 guests)

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts