SOLUTION: Anna took a job that paid $200 the first week. She was guaranteed a raise of 5% each week. How much money will she make in all over 8 weeks? Round the answer to the nearest cent.

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Question 1138441: Anna took a job that paid $200 the first week. She was guaranteed a raise of 5% each week. How much money will she make in all over 8 weeks? Round the answer to the nearest cent.
Thanks!
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
this takes the form of a geometric progression.

in a geometric proression, .....

An = A1 * R ^ (n-1)

Sn = A1 * (1 - R^n) / (1 - R)

since A1 = 200 and n = 8, and R = 1.05, you get:

A8 = 200 * 1.05 ^ 7 = 281.4200845

S8 = 200 * (1 - 1.05^8) / (1 - 1.05) = 1909.821775.

a quick check using excel shows this to be true.

$$$

rounded to the nearest cent, this is equal to 1909.82.