You are looking at a one-year loan of $16,500. the interest rate is quoted as 8.7 percent plus two points. a point on a loan is 1 percent (one percentage point) of the loan amount. quotes similar to this one are common with home mortgages. the interest rate quotation in this example requires the borrower to pay two points to the lender up front and repay the loan later with 8.7 percent interest. what rate would you actually be paying here?

You hold a diversified $100,000 portfolio consisting of 20 stocks with $5,000 invested in each. the portfolio's beta is 1.12. you plan to sell a stock with b = 0.90 and use the proceeds to buy a new stock with b = 1.50. what will the portfolio's new beta be? do not round your intermediate calculations.

David consumes two things: gasoline (g) and bread (b). david's utility function is u(g, b) = 10g^0.25 b^0.75. use the lagrange technique to solve for david's optimal choices of gasoline and bread as a function of the price of gasoline, p_g, the price of bread, p_b, and his income m. with recent decrease in the price of gasoline (maybe due to external shock such as shale gas production) does david increase his consumption of gasoline? for david, how does partial differential g/partial differential p_g depend on his income m? that is, how does david's change in gasoline consumption due to an increase in the price of gasoline depend on his income level? to answer these questions, find the cross-partial derivative, |partial differential^2 g/partial differential m partial differential p_g.

Alpine west, inc., operates a downhill ski area near lake tahoe, california. an all-day, adult ticket can be purchased for $55. adult customers also can purchase a season pass that entitles the pass holder to ski any day during the season, which typically runs from december 1 through april 30. the season pass is nontransferable, and the $450 price is nonrefundable. alpine expects its season pass holders to use their passes equally throughout the season. the company’s fiscal year ends on december 31. on november 6, 2009, jake lawson purchased a season ticket. required: 1. when should alpine west recognize revenue from the sale of its season passes? 2. prepare the appropriate journal entries that alpine would record on november 6 and december 31. 3. what will be included in the 2009 income statement and 2009 balance sheet related to the sale of the season pass to jake lawson?