Answer
The salary for the 7th year is\[\$3,795,957\].
Work Step by Step
: In the first year the salary of the player is \[\$3,000,000\]andan annual year the increment is 4%.
So,
4% of 3000000=4/100* 3000000
=4times 30000
=120000
So, the salary of the player at the starting of the second year is:
\[\$3,000,000+120,000=3,120,000\]
At the starting of the third year, the salary of the player will be the salary in the seconds year increased by 4%.
4% of 3120000=4/100* 3120000
=4*31200
=124800
The salary for the third year is:
\[\$3,120,000+\$124,800=\$3,244,800\]
Now the series is 3000000, 3120000, 3244800……. It is a form of G.P.
The nth term is found in G.P with the help of the following formula
\[{{a}_{n}}=a{{r}^{\left( n-1 \right)}}\]
The salary of the player accumulates according to G.P. with \[a=3000000,\,r=1\cdot 04\] and it is required to find \[{{7}^{th}}\]term.
\[\begin{align}
& {{a}_{n}}=a{{r}^{n-1}} \\
& {{a}_{7}}=3000000\times {{\left( 1.04 \right)}^{\left( 7-1 \right)}} \\
& =3000000\times {{\left( 1.04 \right)}^{6}} \\
& {{a}_{7}}=3795957.06
\end{align}\]
Hence, salary of the player in year 7 rounded to the nearest dollar is\[\$3,795,957\].
