Your older brother turned 35 today, and he is planning to save $90,000 per year for retirement, with the first deposit to be made one year from today. He will invest in a mutual fund that's expected to provide a return of 7.5% per year. He plans to retire 30 years from today, when he turns 65, and he expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can he spend each year after he retires? His first withdrawal will be made at the end of his first retirement 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.

Manipulation manufacturing's (amm) standards anticipate that there will be 5 pounds of raw material used for every unit of finished goods produced. amm began the month of maymay with 8,000 pounds of raw material, purchased 25,500 pounds for $ 15,300 and ended the month with 7,400 pounds on hand. the company produced 4,9004,900 units of finished goods. the company estimates standard costs at $ 1.10 per pound. the materials price and efficiency variances for the month of maymay were:

Acompany has $80,000 in outstanding accounts receivable and it uses the allowance method to account for uncollectible accounts. experience suggests that 6% of outstanding receivables are uncollectible. the current credit balance (before adjustments) in the allowance for doubtful accounts is $1,200. the journal entry to record the adjustment to the allowance account includes a debit to bad debts expense for $4,800. true or false