Justine earned $26,000 during the first year of her job at city hall. After each year she received $26,000 a 3% raise. How do you find her total earnings during the first five years on the job?

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Answer 1 · 2018-01-20T20:16:59

$$29,900$

So her first year she makes $26,000$

The next year she gets a raise of $3%$ or $26,000 xx 0.03$

The year after that she makes $0.03 xx 26,000$ on top of the previous year

And so on and so forth

A trend I notice is that her initial $26,000$ never changes but that $(26,000 + 0.03)$ builds after each year

$color(blue)((26,000 * 5)) + x(26,000 xx 0.03)$

Now let's solve for when $x = color(blue)(5-1 = 4)$

$color(blue)(130000 + 4)(0.03 xx 26,000)$

$color(blue)(130000 + 4(780))$

$color(blue)(130000 + 3120)$

$color(blue)($133120)$

Answer 2 · 2018-01-25T15:07:33

Justine’s total earnings in 5 years $color(brown)(A = $133,120)$

Formula to be used is similar to simple interest.

$I = (P*N*R)/100$ where

P = Earnings per annum, N = No. of years - 1, R = Revision per annum.

N = (No. of years - 1) as during first year will not have any increase

Given $P = $26,000, N = 4 years, R = 3%$

To find $A = P + I$

$I = (P N R) / 100 =((cancel(26000) 260* 4 * 3)/cancel(100))$

$I = (260 * 4 * 3) = 3120 = color(brown)($3,120)$

Total earnings during 5 years $A = (5 * 26000) + 3120 = color(brown)($ 133,120)$