Jane smith has $20,000 in a brokerage account, and she plans to contribute an additional $7,500 to the account at the end of every year. the brokerage account has an expected annual return of 8%. if jane’s goal is to accumulate $375,000 in the account, how many years will it take for jane to reach her goal?

Four analysts cover the stock of fluorine chemical. one forecasts a 6% return for the coming year. the second expects the return to be negative 6%. the third predicts a return of 8%. the fourth expects a 2% return in the coming year. you are relatively confident that the return will be positive but not large, so you arbitrarily assign probabilities of being correct of 35 % comma 8 %, 17 %, and 40%, respectively, to the analysts' forecasts. given these probabilities, what is fluorine chemicals expected return for the coming year

5. profit maximization and shutting down in the short run suppose that the market for polos is a competitive market. the following graph shows the daily cost curves of a firm operating in this market. 0 2 4 6 8 10 12 14 16 18 20 50 45 40 35 30 25 20 15 10 5 0 price (dollars per polo) quantity (thousands of polos) mc atc avc for each price in the following table, calculate the firm's optimal quantity of units to produce, and determine the profit or loss if it produces at that quantity, using the data from the previous graph to identify its total variable cost. assume that if the firm is indifferent between producing and shutting down, it will produce. (hint: you can select the purple points [diamond symbols] on the previous graph to see precise information on average variable cost.) price quantity total revenue fixed cost variable cost profit (dollars per polo) (polos) (dollars) (dollars) (dollars) (dollars) 12.50 135,000 27.50 135,000 45.00 135,000 if the firm shuts down, it must incur its fixed costs (fc) in the short run. in this case, the firm's fixed cost is $135,000 per day. in other words, if it shuts down, the firm would suffer losses of $135,000 per day until its fixed costs end (such as the expiration of a building lease). this firm's shutdown price—that is, the price below which it is optimal for the firm to shut down—is per polo.

Which of the following statements is true of unsought products? as compared to convenience products, unsought products are purchased more frequently. unsought products are consumer products and services that customers usually buy frequently, immediately, and with minimal comparison and buying effort. a life insurance policy is an example of an unsought product. unsought products have strong brand identification for which a significant group of buyers is willing to make a special purchase effort. unsought products are those products purchased for further processing or for use in conducting a business.