Problem $8-14($Algo$)$ Dollar$-$value LIFO $[$LO$8-8]$

A company uses the dollar$-$value LIFO method of computing inventory. An external price index is used to convert ending inventory to base year. The company began operations on January $1,2024,$ with an inventory of $$265,000.$ Year$-$end inventories at year$-$end costs and cost indexes for its one inventory pool were as follows:

$\backslash$table$[[\backslash$table$[[$Year Ended$],[$December $31]],\backslash$table$[[$Ending Inventory at$],[$Year$-$End Costs$]],\backslash$table$[[$Cost Index $($Relative to$],[$Base Year$)]]],[2024,$$$336,600,1\mathrm{.}02],[2025,427,350,1\mathrm{.}11],[2026,405,000,1\mathrm{.}08],[2027,395,200,1\mathrm{.}04]]$

Required:

Calculate inventory amounts at the end of each year.

Note: Round intermediate calculations and final answers to the nearest whole dollars.

$\backslash$table$[[$Date$,\backslash$table$[[$Inventory Layers Converted$],[$to Base Year Cost$]],$Inventory Layers Converted to Cost,$\backslash$table$[[$Inventory DVL$],[$Cost$]]],[\backslash$table$[[$Inventory at$],[$Year$-$End$],[$Cost$]],\backslash$table$[[$Inventory$],[$Layers at$],[$Base Year$],[$Cost$]],,\backslash$table$[[$Inventory$],[$Layers at Base$],[$Year Cost$]],\backslash$table$[[$Inventory$],[$Layers$],[$Converted to$],[$Cost$]]],[01/01/2024,,,$Base,,,$],[12/31/2024,,,$Base,,,$],[,,2024,,,],[12/31/2025,,,$Base,,,$],[,,2024,,,],[,,2025,,,],[12/31/2026,,,$Base,,,$],[,,2024,,,],[,,2025,,,],[,,2026,,,],[12/31/2027,,,$Base,,,$],[,,2024,,,],[,,2025,,,],[,,2026,,,],[,,2027,,,]]$