Question

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?

Answer 1

`$29,900`

Explanation:

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

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

Explanation:

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)`