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Adam earns $45,000 in his first year as an accountant and earns a 3% increase in each

successive year.

(a) Write a geometric series formula,

n S

, for Adam’s total earnings over

n

years.

(b) Use this formula to find Adam’s total earnings for her first 12 years of his job, to the nearest

cent.

Respuesta :

Answer:

$638641.33

Step-by-step explanation:

Adam earns $45,000 in his first year.

His salary increases by 3% each successive year. Therefore, his salary the next year is 103% of his previous year.

This is a geometric sequence where the:

  • First Term, a= $45,000
  • Common ratio, r =103%=1.03

(a)

Sum of  geometric series[tex]=\dfrac{a(r^n-1)}{r-1}[/tex]

Substituting the given values, Adam's total earnings over n years

[tex]=\dfrac{45000(1.03^n-1)}{1.03-1}\\\\$Adam's Total Earnings=\dfrac{45000(1.03^n-1)}{0,03}[/tex]

(b)When n=12 years

[tex]\text{Adam's Total Earnings for the first 12 years=}\dfrac{45000(1.03^{12}-1)}{0.03}\\=\$638641.33$ (correct to the nearest cent)[/tex]

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