Based on the information below, please answer Question $18$ and Question $19$:

On January $1,2018,$ Empire, Inc. adopted the dollar$-$value LIFO method of computing inventory. An internal cost index is used to convert ending inventory to base year. Inventory on January $1$ was $$350,000.$ Year$-$end inventories at year$-$end costs and cost indexes for its one inventory pool were as follows:

$\backslash$table$[[$Year Ended December $31,$Inventory at Year$-$end Costs,Cost Index $($Relative to Base Year$)],[2018,$$$383,250,1\mathrm{.}05],[2019,419,650,1\mathrm{.}09],[2020,427,500,1\mathrm{.}14]]$

REQUIRED: Calculate the ending balance for Inventory for the year ended December $31,2020.$ Show all work and clearly highlight your final answer.