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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.

Respuesta :

mhanifa

Answer:

  • 7 years

Step-by-step 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

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