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4 August, 09:24

In his first year, a math teacher earned $32,000. Each successive year, he

earned a 5% raise. How much did he earn in his 20th year? What were his total

earnings over the 20-year period?

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Answers (1)
  1. 4 August, 13:11
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    Step-by-step explanation:

    Each successive year, he

    earned a 5% raise. It means that the salary is increasing in geometric progression. The formula for determining the nth term of a geometric progression is expressed as

    Tn = ar^ (n - 1)

    Where

    a represents the first term of the sequence (amount earned in the first year).

    r represents the common ratio.

    n represents the number of terms (years).

    From the information given,

    a = $32,000

    r = 1 + 5/100 = 1.05

    n = 20 years

    The amount earned in his 20th year, T20 is

    T20 = 32000 * 1.05^ (20 - 1)

    T20 = 32000 * 1.05^ (19)

    T20 = $80862.4

    To determine the his total

    earnings over the 20-year period, we would apply the formula for determining the sum of n terms, Sn of a geometric sequence which is expressed as

    Sn = (ar^n - 1) / (r - 1)

    Therefore, the sum of the first 20 terms, S20 is

    S20 = (32000 * 1.05^ (20) - 1) / 1.05 - 1

    S20 = (32000 * 1.653) / 0.05

    S20 = $1057920
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