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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.

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

BFor each company find the sum of wages earned during the first 20 years of employment

Cusing 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?

Verified Answer :

nobillionaireNobley

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.