Companies A and B purchased identical equipment having an estimated service life of $10$ years. Company A uses straight$-$line amortization, and Company B uses sum$-$of$-$the$-$years'$-$digits. Assuming that the companies are identical in all other respects, choose the correct statement below:

Multiple Choice

At the end of the third year, the book value of the asset will be lower on the books of Company A than on the books of Company B$.$

Net income will be lower for Company A in the ninth year than for Company B$.$

Amortization expense for Company A will be higher in the first year than for Company B$.$

Company B will record more amortization on this asset over the entire $10$ years than will Company A