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d1i1m1o1n [39]
3 years ago
10

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 n

umber of years ‘n’ until you will have earned a total of $321,000 since starting this job.
Mathematics
1 answer:
LuckyWell [14K]3 years ago
3 0

Answer:

  • 7 years

Step-by-step explanation:

<u>This is going to be an arithmetic progression:</u>

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

<u>So the first term is </u>

  • a₁ = 48500

<u>and the common difference is </u>

  • d = 1200

<u>Sum of AP is:</u>

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

<u>Substitute and solve for n:</u>

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

<u>Solving we get a positive root of:</u>

  • n ≈ 6.21 and it rounds up to 7 years

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