USAA, the United Services Automobile Association, is a diversified financial services group of companies based in San Antonio, Texas. Currently, ranked 52nd in net worth and 100th in revenue in Fortune 500 companies, USAA offers banking, investing, and insurance to people and families that serve, or served, in the U.S. military. At the end of last year, there were 12.4 million members, 50.7 million products, and 32,700 employees. It is the 4th largest homeowners' insurer and the 5th largest auto insurer.
USAA was founded in 1922 by 25 army officers who came together in San Antonio and decided to insure each other's automobiles. In the 1930s, even with the Great Depression, the number of employees doubled from 46 to 99. By 1940, there were 30,000 members including 60% of all eligible U.S. military officers. During the 1940s, in spite of a decrease in driving due to wartime restrictions on gasoline, spare parts, and tires, USAA grew rapidly and reported a profit of over $3 million. At the end of the 1950s, profits were over $14 million. In 1961, USAA's bylaws were changed such that membership no longer had to be relinquished when an officer leaves the service. In 1963, the USAA Life Insurance Company was formed; and by the end of 1969, there were 700,000 members producing a profit of almost $24 million.
In 1977, USAA reached $1 billion in assets; and in 1983 they opened the USAA Federal Savings Bank. Fortune magazine named USAA one of "America's Most Admired Companies" in 1992 and Money magazine named USAA Federal Savings Bank the best bank in America. By the turn of the century, USAA owned and operated a total of $58.9 billion assets. By 2003, 96% of all active-duty officers and 44% of enlisted personnel were USAA members. USAA introduced a car-buying service in 2008; and in 2009, the company expanded its eligibility to all who are serving or have honorably served our nation in the U.S. military and their families. In 2011, Fortune magazine included USAA on its list of "100 Best Companies to Work For" for the third straight year.
According to their mission statement, "USAA's mission is to facilitate the financial security of its members, associates and their families by providing a full range of highly competitive financial products and services. In so doing, we seek to be the provider of choice for the military community." Discussion
1. According to the National Association of Insurance Commissioners (NAIC), the average premium for homeowner's insurance in the United States in a recent year was $1,034. Suppose these premium rates are uniformly distributed across the country from $535 to $1,533. What percentage rates are between $800 and $1,200? What percentage are more than $1,350?
2. A study by Quadrant Information Services commissioned by Insure.com calculated auto insurance rates for each of the 50 states; and as a result, the average annual rate for the United States was $1,317. Suppose annual rates of auto insurance in the United States are normally distributed with a standard deviation of $324. Based on these data, what is the probability that a randomly selected auto insurance rate in the United States would be greater than $1,750? What percentage of auto insurance rates would be less than $1,200? What percentage of auto insurance rates would be between $1,100 and $1,500?
3. Homeowners do not make insurance claims very often. In fact, the Oregon Insurance Division says that, on average, a homeowner makes one claim every 9 years. Suppose such homeowner claims are Poisson distributed. What is the probability that it would be 15 years or more between claims for a homeowner? What percentage of the time would it be less than 5 years between claims? According to data released by the Insurance Information Institute, the claim frequency for automobile collisions is 5.59 per 100 car years (a car year is equal to 365 days of insured coverage for one vehicle). What is the average "interarrival time" for auto collisions in car years? What do you think this average means? Assume that auto collisions are Poisson distributed.