Answer
The company B pay more as compare to company A.
Work Step by Step
Case 1:
Company A
Starting salary is\[\$20,000\].
Increment per year is\[\$1000\].
So, the salary year by year is;
\[\$20000,\$21000,\$22000,\$23000,\ldots\]
It is a form of A.P.
Where \[a=\$20000\]and the common difference \[d=\$1000\]
It is known that the nth term in A.P is;
\[{{a}_{n}}=a+\left( n-1 \right)d\]
And,
\[\begin{align}
& {{a}_{7}}=20000+\left( 6-1 \right)1000 \\
& =20000+5\times 1000 \\
& =20000+5000 \\
& =25000
\end{align}\]
Case 2:
Company B
Starting salary is\[\$20,000\].
Increment per year \[5%\] of salary;
\[\frac{5}{100}\times 20000=1000\]
So, the salary of the starting of second year is \[21000\].
Salary of the staring of third year is;
\[\begin{align}
& 21000+\left( \frac{5}{100}\times 21000 \right)=21000+1050 \\
& =22050
\end{align}\]
Salary of the staring of fourth year is;
\[\begin{align}
& 22050+\left( \frac{5}{100}\times 22050 \right)=22050+1102.5 \\
& =23152.5
\end{align}\]
Salary of the staring of fifth year is;
\[\begin{align}
& 23152.5+\left( \frac{5}{100}\times 23152.5 \right)=23152.5+1157.6 \\
& =24310.1
\end{align}\]
Salary of the staring of sixth year is;
\[\begin{align}
& 24310.1+\left( \frac{5}{100}\times 24310.1 \right)=24310.1+1215.5 \\
& =25525.60
\end{align}\]
Hence, the company B pay more as compare to company A.
