Answer
Total salary over 5 years by company A = 169112.8
Total salary over 5 years by company B = 169892.3
Company B offers better total salary for a five year contract.
Company B offers = 779.5 more than company A.
Work Step by Step
Company A offers salary on first year $a_{1}$ = 30000
As company A increase salary 6% each year means the salary multiply by 1.06 each year, so common ratio = 1.06
Total salary calculated for 5 years then n = 5
Total salary over n years is given by sum formula $S_{n}$ = $a_{1}$$\frac{(1 - r^{n})}{(1 - r)}$
Total salary over 5 years by company A $S_{5}$ = 30000$\frac{(1 - 1.06^{5})}{(1 - 1.06)}$
= 30000$\frac{(1 - 1.338)}{(1 - 1.06)}$
= 30000$\frac{(-0.338)}{(-.06)}$
= 30000$\times$5.64 = 169112.8
Company B offers salary on first year $a_{1}$ = 32000
As company B increase salary 3% each year means the salary multiply by 1.03 each year, so common ratio = 1.03
Total salary calculated for 5 years then n = 5
Total salary over n years is given by sum formula $S_{n}$ = $a_{1}$$\frac{(1 - r^{n})}{(1 - r)}$
Total salary over 5 years by company B $S_{5}$ = 32000$\frac{(1 - 1.03^{5})}{(1 - 1.03)}$
= 32000$\frac{(1 - 1.159)}{(1 - 1.03)}$
= 32000$\frac{(-0.159)}{(-.03)}$
= 32000$\times$5.31 = 169892.3
Total salary over 5 years by company A = 169112.8
Total salary over 5 years by company B = 169892.3
Company B offers better total salary for a five year contract.
Company B offers 169892.3 - 169112.8 = 779.5 more than company A.