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?

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?

dumbcow · Answer

Company A:
arithmetic series: An = 20,000 + 1000(n-1)
A_20 = 39,000
sum after 20 years: Sn = 20(20,000+39,000)/2 = 590,000

Company B:
geometric series: An = 20,000(1.04)^(n-1)
A_20 = 42,136.98
sum after 20 years: Sn = 20,000(2.1911 -1)/(1.04-1) = 595,561.57