Question

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.

Answer 1

$638641.33

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
`=(a(r^n-1))/(r-1)`

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

`=(45000(1.03^n-1))/(1.03-1)\\\\$Adam's Total Earnings=(45000(1.03^n-1))/(0,03)`

(b)When n=12 years

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