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- Suppose a company charges a premium of $150 per year for an insurance policy for storm damage to roofs. Actuarial studies show that in case of a storm, the insurance company will pay out an average of $8000 for damage to a composition shingle roof and an average of $12,000 for damage to a shake roof. They also determine that out of every 10,000 policies, there are 7 claims per year made on composition shingle roofs and 11 claims per year made on shake roofs. What is the company’s expected value (i.e., expected profit) per year of a storm insurance policy? What annual profit can the company expect if it issues 1000 such policies? Determine the probability of a composition shingle roof claim out of 10,000 = ______ Determine the probability of a shake roof claim out of 10,000 = ______ How many claims are made out of 10,000? = _______ What is the probability of no claims out of 10,000? = _______ How much does each shingle roof claim cost the company, don’t forget each person pays $150…In winter of a country, it rains 45% of the days and shine 55% of the days. Mr. X has abarometer which wrongly predicts 5% of the time in rainy days and 10% on shiny days.Mr. X does not carry umbrella if barometer predicts shine. On good shiny morning inwinter, his barometer predicts “shine” and he does not carry umbrella. What is theprobability that Mr. X will suffer from rain on that day.A project requires an initial outlay of $92000 and produces a return of $30000 at the end of year 1, $40000 at the end of year 2, and $42xyz at the end of year 3, where x, y, z are the last three digits of your student code (for example: if a student code is 17071365 then x = 3, y = 6, z = 5 and $42xyz=$42365). a/ Use the trial-and-error method or another appropriate method to determine the internal rate of return IRRof the project (express IRR in percentage, rounded to one decimal place); b/ Find the net present value NPV of the project if the market rate r is equal to the value of IRR as found above, then give a comment.