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Studentka2010 [4]
2 years ago
11

Alexander was offered a job that paid a salary of $24,000 in its first year. The salary was set to increase by 4% per year every

year. If Alexander worked at the job for 5 years, what was the total amount of money earned over the 5 years, to the nearest whole number?
Mathematics
1 answer:
qwelly [4]2 years ago
5 0

9514 1404 393

Answer:

  $129,992

Step-by-step explanation:

The sum of a geometric series is given by ...

  Sn = a1·(r^n -1)/(r -1)

Here, the first term is 24000, and the growth factor r is 1+4% = 1.04. The sum is then ...

  S5 = 24000·(1.04^5 -1)/(1.04 -1) ≈ 129992

The total earned over 5 years was $129,992.

___

A spreadsheet can list the annual salaries and add them up. The salary each year is 1.04 times that of the previous year. That is shown in the attachment.

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y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\Let \ us\ use\ the\ points\  (1,55)\ and\ (3,105),hence:\\\\y-55=\frac{105-55}{3-1}(x-1)\\\\y-55=25(x-1)\\\\y=25x-25+55 \\\\y=25x+30\\\\For\ 10\ months(i.e.\ x=10):\\\\y=25x+30\\\\y=25(10)+30\\\\y=\$28 0

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