The number of years n required for an investment at interest rate r to double in value must satisfy (1 + r)n = 2. Using ln 2 = .69 and the approximation ln(1 + r) ≈ r valid for small r, show that n ≈ 69/i, where i is the interest rate percentage (that is, i = 100r). Using the better approximation ln(1+r) ≈ r − 1 2 r2, show that for r ≈ .08 there holds n ≈ 72/i.

Daniel owns 100 shares of abc corporation's common stock. abc uses the fair value option, and recent declines in the firm's credit rating have caused the value of the firm's outstanding bonds payable to drop by 10%. daniel feels this is good news, but he wants to know what you think about the situation. which of the following represents your best response? a : "this situation may be positive for you in that the change in abc's credit standing indicates that the value of the firm's assets is likely increasing. however, the drop in bond value may negate any positive effects on your bottom line, because it means your claim on the firm's assets is simultaneously decreasing." b : "actually, this is bad news all around. the drop in the value of abc's bonds payable means shareholders' claims on the firm's assets have decreased. moreover, abc's declining credit rating means that the firm's assets are probably also dropping in value, thus magnifying your losses even more." c : "on the surface, this seems like good news because it means your claim on the firm's assets has increased. however, the drop in creditworthiness may also indicate that abc's assets are declining in value, thus offsetting any gains associated with the drop in bonds payable." d : "you're right! this is good news because it means that abc's debtholders have a decreased claim on the firm's assets. as a result, the firm's existing shareholders"like you"have seen their claim on the firm's assets increase."

Why entrepreneurs start businesses. a) monopolistic competition b) perfect competition c) sole proprietorship d) profit motive

Elite coffee and bakery, a café that offers a relaxing environment to enjoy quality coffees, teas, soups, and other menu items, has a poster in the front of its restaurants that reads, "we will always provide a quality product to our customers better meet the challenges of their day and always take the time to offer caring service one person at a time." this statement is elite's