Question

Two companies Company A and Company B offer the same starting salary of $20,000 per year. Company A gives a raise of $1000 each year.Company B gives a raise of 4% each year.

a) Write rules a and b in the nth year at companies A and B respectively.

b) For each company find the sum of wages earned during the first 20 years of employment

c) using the graphing calculator to find after how many years the total amount earned a company B is greater that the total amount of earned at company A?

Answer 1

a.) A = 20000 + 1000n
B = 20000(1.04)^n

b.) For A, sn = n/2(2a + (n - 1)d)
s20 = 20/2(2(20000) + 1000(20 - 1)) = 10(40000 + 19(1000)) = 10(40000 + 19000) = 10(59000) = $590,000
For B, sn = a(r^n - 1)/(r - 1)
s20 = 20000((1.04)^20 - 1)/(1.04 - 1) = 20000(2.191 - 1)/0.04 = 20000(1.191)/0.04 = 23822.46 / 0.04 = $595,561.57

c.) Using a graphing calculator, it takes 18 years for the
total amount earned a company B is greater that the total amount of earned at company A.