$7.$ A company adopted dollar$-$value LIFO $($DVL$)$ as of January $1,2024,$ when the inventory value was $$500,000$ and the cost index was $1\mathrm{.}0.$ On December $31,2024,$ the inventory value at year$-$end costs was $$535,000$ and the cost index was $1\mathrm{.}06.$ The company would report a LIFO inventory of:

a$.$ $$533,019$

b$.$ $$504,717$

c$.$ $$505,000$

d$.$ $$527,619$