A new employee is offered two salary package Both start with

A new employee is offered two salary package. Both start with an initial annual salary of $32,000. Package offers a $4000 salary Increase each year. Package B offers a 1021% salary increase each year. (a) Write the first four terms of the sequence, a_n of yearly salaries for each package, a_1, is the salary for the first (initial) year. Round your answers for Package R to the nearest integer. Package A: a_1 = a_2 = a_3 = a_4 = Package B: a_1 = a_2 = a_3 = a_4 = (b) After how many years will Package B pay a higher annual salary than Package A? Package B pays a higher annual salary than Packaged after years.

Solution

Package A

a1 = $32000, a2 = $36000, a3 = $40000, a4 = $44000

package B,

a1 = $32000, a2 = $32000 x 1.1021 = $35267.2,

a3 = $35267.2 x 1.1021 = $38867.98 , a4 = $38867.98 x 1.1021 = $42836.4

b) let after n year,

32000 x (1.1021)ⁿ > 32000 + 4000n

8 (1.1021)ⁿ > 8 + n

(1.1021)ⁿ > 1 + (n/8)

n = 5 years