Instructions

Please submit all work via Excel spreadsheets. Clearly articulate all assumptions and

calculations. Identify each key cell used in your calculations.

Overview for Problems $1-4$

IRM Insurance Company recently launched a new renters insurance product. They

expect to sell $50,000$ renters insurance policies that pay a benefit of $$10,000$ when a

loss occurs. All insured risks are identical and independent. Based on research, the

Pricing actuaries at IRM Insurance Company believe the probability of loss equal is

equal to $1\mathrm{.}0\%$ and the variance of loss is equal to $5\mathrm{.}0\%.$

Questions:

$(3$ points$)$ What is the number and amount of claims that IRM Insurance

Company can expect to pay?

$(3$ points$)$ What premium should IRM Insurance Company charge per policy to

cover only expected losses?

$(5$ points$)$ What extra premium should the IRM Insurance Company charge each

policyholder to cover losses with $97\mathrm{.}5\%$ of certainty?

$(6$ points$)$ After speaking to the sales agents IRM Insurance Company decides to

update their expected sales assumption to $100,000$ policies. If IRM still wants to

cover losses with $97\mathrm{.}5\%$ certainty $-$ how much extra premium should they

charge now? Explain why there is a difference is the answer to this question vs$.$

question #$3.$