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Chapter 14: Problem 64

Company A pays \(\$ 23,000\) yearly with raises of \(\$ 1200\) per year. Company B pays \(\$ 26,000\) yearly with raises of \(\$ 800\) per year. Which company will pay more in year \(10 ?\) How much more?

Short Answer

Expert verified
Company B will pay more in the 10th year. The difference in the salary paid by Company B and Company A after 10 years is \$15,000.

Step by step solution

01

Understanding the Problem and Decoding the Information Provided

Company A: Initial Yearly Salary (a1): \$23,000; Increase in Salary each year (d): \$1200; Total Years (n): 10 Company B: Initial Yearly Salary (a1): \$26,000; Increase in Salary each year (d): \$800; Total Years (n): 10
02

Calculation of the total salary for Company A

Every year's salary at company A is an arithmetic progression with the first term as \$23000 and a common difference of \$1200. The sum of an arithmetic progression is given by the formula \(S = n / 2 * (2a + (n - 1) d)\) where S is the total salary, n is the number of years, a is the initial salary, and d is the yearly increment. So the total salary from company A after 10 years is: \(S_{A} = 10 / 2 * (2* 23000 + (10 - 1) * 1200) = \$265,000.
03

Calculation of the total salary for Company B

Similarly, for Company B, with a starting salary of \$26000 and yearly increments of \$800 for the next 10 years, the total salary is: \(S_{B} = 10 / 2 * (2 * 26000 + (10 - 1) * 800) = \$280,000.
04

Comparing the total salaries

Now comparing the total salaries of Company A and Company B over 10 years, it can be seen that Company B pays more over 10 years.
05

Calculating the Difference

The difference in the total salaries paid by Company B and Company A is: \(Difference = S_B - S_A = \$280,000 - \$265,000 = \$15,000

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