Exercise $8\mathrm{.}7($Algo$)$ Costing Inventory in a Periodic System $($LO $8-4)$

Rogers Products uses a periodic inventory system. The company$$s records show the beginning inventory of PH$4$ oil filters on January $1$ and the purchases of this item during the current year to be as follows.

Jan. $1$ Beginning inventory $13$ units @ $ $3\mathrm{.}00$ $ $39\mathrm{.}00$

Feb. $23$ Purchase $14$ units @ $ $3\mathrm{.}5049\mathrm{.}00$

Apr. $20$ Purchase $32$ units @ $ $3\mathrm{.}80121\mathrm{.}60$

May $4$ Purchase $40$ units @ $ $4\mathrm{.}00160\mathrm{.}00$

Nov. $30$ Purchase $19$ units @ $ $5\mathrm{.}0095\mathrm{.}00$

Totals $118$ units $ $464\mathrm{.}60$

A physical count indicates $23$ units in inventory at year$-$end.

Determine the cost of the ending inventory on the basis of each of the following methods of inventory valuation. $($Remember to use periodic inventory costing procedures.$)($Round your intermediate and final answers to $2$ decimal places.$)$

a$.$ Average cost

b$.$ FIFO

c$.$ LIFO