A job pays a salary of 24000 the first year During the next

A job pays a salary of $24,000 the first year. During the next 10 years, the salary increases by 4% each yaer. What is the total lifetime salary over the 11-years period?

The total lifetime dalary is approximately $ [ ]. (do not round until the dinal answer. Then round to the nearest dollar as needed.)

Solution

The salary in the first year is $ 24000. The salary in the 2^nd year is $ 24000 + $ 24000* 0.04= $ 24000(1.04). The salary in the 3^rd year is $ 24000*1.04*1.04 and so on. The series 24000, 24000*1.04, 24000*1.04*1.04,… is a geometric series. We know that, for a geometric sequence with first term a and common ratio r ( r > 1), the sum ( S ) of the first n terms is given by: S = a( rⁿ – 1))/( r - 1). Here, a = 24000, r = 1.04 and n = 11 (Remember that the question mentions next 10 years).Therefore, S = 24000[(1.04)¹⁰ – 1]/ (1.04 –1) = 24000( 1.480244285 -1)/( 0.04) = (24000* 0. 480244285 )/ 0.04 = $ 288146.57 = $ 288147 ( on rounding off to the nearest Dollar). Thus, the lifetime salary over the 11 years period is $ 288147.