Question

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

Answer 1

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$=\dfrac{a(r^n-1)}{r-1}$

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

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

(b)When n=12 years

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