Sequence and Series - Problems involving inequalities

A company offers its employees a choice of two salary schemes \(\mathrm{A}\) and \(\mathrm{B}\) over a period of \(10\) years.

Scheme \(\mathrm{A}\) offers a starting salary of \(\$ 11 \ 000\) in the first year and then an annual increase of \(\$ 400\) per year.

1. 1. Write down the salary paid in the second year and in the third year.
   2. Calculate the total (amount of) salary paid over ten years.

Scheme \(\mathrm{B}\) offers a starting salary of \(\$10 \ 000\) dollars in the first year and then an annual increase of \(7 \%\) of the previous year's salary.

2. 1. Write down the salary paid in the second year and in the third year.
   2. Calculate the salary paid in the tenth year.
3. Arturo works for \(n\) complete years under scheme \(\mathrm{A}\). Bill works for \(n\) complete years under Scheme \(\mathrm{B}\). Find the minimum number of years so that the total earned by Bill exceeds the total earned by Arturo.