Question

Suppose you received a job offer with a starting salary of $48,500 per year and a guaranteed raise of $1200 per year. Find the number of years ‘n’ until you will have earned a total of $321,000 since starting this job.

Answer 1

• 7 years

Explanation:

This is going to be an arithmetic progression:

• 48500, 48500 + 1200, 48500 + 1200*2, ...

So the first term is

• a₁ = 48500

and the common difference is

• d = 1200

Sum of AP is:

• S = (a₁ + aₙ)*n/2 = (2a₁ + (n - 1)d)*n/2

Substitute and solve for n:

• (2*48500 + (n - 1)*1200)*n/2 = 321000
• (97000 + 1200n - 1200)n = 642000
• 1200n² + 95800n - 642000 = 0
• 6n² + 479n - 3210 = 0

Solving we get a positive root of:

• n ≈ 6.21 and it rounds up to 7 years