The present value of an annuity is the sum of the discounted value of all future cash flows.
You have the opportunity to invest in several annuities. Which of the following 10-year annuities has the greatest present value (PV)?

a. An annuity that pays $1, 000 at the beginning of each year.
b. An annuity that pays $1, 000 at the end of each year.
c. An annuity that pays $500 at the end of every six months.
d. An annuity that pays $500 at the beginning of every six months.

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.

Portia grant is an employee who is paid monthly. for the month of january of the current year, she earned a total of $8,388. the fica tax for social security is 6.2% of the first $118,500 earned each calendar year and the fica tax rate for medicare is 1.45% of all earnings. the futa tax rate of 0.6% and the suta tax rate of 5.4% are applied to the first $7,000 of an employee's pay. the amount of federal income tax withheld from her earnings was $1,391.77. what is the total amount of taxes withheld from the portia's earnings?

If ming wants a tertiary color, she should combine