Suppose you begin a job with an annual salary of $45,900. Each year you are assured of a 3.5% raise. After how many years will you have earned a total of $1,000,000

A) 16 years

B) 17 years

C) 18 years

D) 19 years

Question

Mathematics

Natalia Collins

14 October, 01:05

Suppose you begin a job with an annual salary of $45,900. Each year you are assured of a 3.5% raise. After how many years will you have earned a total of $1,000,000

A) 16 years

B) 17 years

C) 18 years

D) 19 years

+1

Answers (1)

Know the Answer?

Monica · Answer 1

Total earnings are the sum of a geometric series:

45900 + 45900 (1.035) + 45900 (1.035) ^2 + ... 45900 (1.035) ^ (n-1)

The sum of this series is:

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

1,000,000 = (45,900) (1.035^n - 1) / (1.035 - 1)

n = 16.47 years

This means that the correct answer is 17 years (B). Note that after 16 years, the sum will not yet have reached 1,000,000.

Suppose you begin a job with an annual salary of $45,900. Each year you are assured of a 3.5% raise. After how many years will you have earned a total of $1,000,000A) 16 yearsB) 17 yearsC) 18 yearsD) 19 years

Suppose you begin a job with an annual salary of $45,900. Each year you are assured of a 3.5% raise. After how many years will you have earned a total of $1,000,000

A) 16 years

B) 17 years

C) 18 years

D) 19 years