MATH SOLVE

4 months ago

Q:
# Suppose you begin a job with an annual salary of $32,900. Each year you are assured of a 5.5% raise. What its the total amount that you can earn in 15 years? A) $34,815 B) $51,751 C) $737,245 D) $1,682,920

Accepted Solution

A:

Answer: the total amount that you can earn in 15 years is $737245. Option CStep-by-step explanation:You receive an annual salary of $32,900 and each year, you are assured of a 5.5% raise. Assuming there was no raise, you get 100% of your previous salary each year. With a raise of 5.5%, you will get 100 + 5.5 = 105.5% of your previous salary for each year. This is a geometric progression and we want to determine the sum of 15 terms(15 years).The formula for the sum of terms in a geometric progression is Sn = [a(r^n - 1)]/ r - 1Sn = sum of n termsa = the first termn = number of termsr = common ratioFrom the information given,a = 32900n = 15r = 105.5/100 = 1.055S15 = [32900(1.055^15 - 1)] / 1.055 - 1S15 = [32900(2.23247649 - 1)] / 0.055S15 = 32900 Γ 1.23247649) / 0.055S15 = 737245.0277S15 = $737245