$13.$ Bond Company adopted the dollar$-$value LIFO inventory method on $12/31/2021.$ The following data was available for $2022$ inventory using this method:

Step $1$ Deflate inventory Step $2$ Inventory Layers Step $3$ Re$-$inflate for Ending Inventory

$12/31/2022$ $$320,000$ $$300,000$ Yr $2021$ $$300,000$ Yr $2021$ x $1\mathrm{.}00$ $$300,000$

$$20,000$ Yr $2022$ $$20,000$ Yr $2022$ x $1\mathrm{.}08$ $$324,000$

$$624,000$

$12/31/2023???????$

If ending inventory at year$-$end cost at $12/31/2023$ is $$420,000$ and the cost index for $2023$ is $1\mathrm{.}20,$ what is the correct ending inventory for $12/31/2023$ under the dollar$-$value LIFO method?

a$.$ $$357,600$

b$.$ $$350,000$

c$.$ $$351,600$

d$.$ None of these is correct