What is the present value of a 10-year annuity of $3,000 per period in which payments come at the beginning of each period? the interest rate is 12 percent.

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.

On january 15, the end of the first biweekly pay period of the year, north company’s payroll register showed that its employees earned $32,000 of sales salaries. withholdings from the employees’ salaries include fica social security taxes at the rate of 6.2%, fica medicare taxes at the rate of 1.45%, $3,000 of federal income taxes, $772 of medical insurance deductions, and $260 of union dues. no employee earned > $7,000 in this first period. prepare the journal entry to record north company’s january 15 (employee) payroll expenses and liabilities.

Under t, the point (0,2) gets mapped to (3,0). t-1 (x, y) →