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The starting salary for a job is €24 000 per annum - Leaving Cert Mathematics - Question b - 2010

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The starting salary for a job is €24 000 per annum. At the end of each year of employment the annual salary increases by 3%. (i) What will the annual salary be afte... show full transcript

Worked Solution & Example Answer:The starting salary for a job is €24 000 per annum - Leaving Cert Mathematics - Question b - 2010

Step 1

What will the annual salary be after the first increase?

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Answer

To calculate the annual salary after the first increase, we start with the initial salary of €24,000. The annual increase is 3% of the current salary.

We can calculate this as follows:

  1. Calculate the increase: extIncrease=0.03imes24000=720 ext{Increase} = 0.03 imes 24000 = 720

  2. Add the increase to the initial salary: extNewSalary=24000+720=24720 ext{New Salary} = 24000 + 720 = 24720

Thus, the annual salary after the first increase will be €24,720.

Step 2

What will the annual salary be after the fourth increase? Give your answer correct to the nearest euro.

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Answer

For the fourth increase, we need to account for the compound increases over four years. The formula for the salary after multiple percentage increases can be expressed as:

extFinalSalary=extInitialSalaryimes(1+r)n ext{Final Salary} = ext{Initial Salary} imes (1 + r)^n

Where:

  • r=0.03r = 0.03 (3% increase)
  • n=4n = 4 (number of increases)

Inserting the values:

extFinalSalary=24000imes(1+0.03)4=24000imes(1.03)4 ext{Final Salary} = 24000 imes (1 + 0.03)^4 = 24000 imes (1.03)^4

  1. Calculate the value: extFinalSalary=24000imes1.12550881approx27012.21 ext{Final Salary} = 24000 imes 1.12550881 \\approx 27012.21

Rounding to the nearest euro, the annual salary after the fourth increase will be €27,012.

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