A woman made $35,000 during the first year of her new job at city hall. Each year she received a 10% raise. How do you find her total earnings during the first eight years on the job?

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Answer 1 · 2016-05-02T19:53:41

Total earnings after 8 years = $400,256.08

Her salary which increases every year forms a geometric sequence.

35,000 ; 38,500 ; 42,350 .......

The common ratio is 1.1. (this can be found by dividing $(T_3)/(T_2)$ )

or by realising that adding 10% onto 100% is the same as multiplying by $110/100$ which is the same as 1.1.

We are asked for her total earnings over 8 years. This now represents a geometric series:

35,000 + 38,500 + 42,350 + .......

There is a formula for the sum of the terms: $S_n = (a(r^n-1))/(r-1)$

$S_8 = (35000(1.1^8 -1))/(1.1-1)$ = $400,256.08