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21 April, 18:39

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

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  1. 21 April, 20:02
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    Answer: the total amount that you can earn in 15 years is $737245. Option C

    Step-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 - 1

    Sn = sum of n terms

    a = the first term

    n = number of terms

    r = common ratio

    From the information given,

    a = 32900

    n = 15

    r = 105.5/100 = 1.055

    S15 = [32900 (1.055^15 - 1) ] / 1.055 - 1

    S15 = [32900 (2.23247649 - 1) ] / 0.055

    S15 = 32900 * 1.23247649) / 0.055

    S15 = 737245.0277

    S15 = $737245
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