Math

QuestionShannon has job offers: Company ABC: \$45,500 with 8\% raise yearly; Company XYZ: \$62,000 with 3\% raise. After 15 years, which is better?

Studdy Solution

STEP 1

Assumptions1. Company ABC offers a starting salary of \$45,500 with an8\% annual raise. Company XYZ offers a starting salary of \$62,000 with a3\% annual raise3. Shannon wants to compare the salaries at the end of15 years4. The annual raises are compounded yearly

STEP 2

First, we need to calculate the salary from Company ABC at the end of15 years. We can use the formula for compound interest, which isA=(1+r/n)ntA = (1 + r/n)^{nt}Here, is the principal amount (the starting salary), r is the annual interest rate (the annual raise), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
In this case, the interest is compounded once per year, so n =1.

STEP 3

Now, plug in the given values for the starting salary, annual raise, and number of years to calculate the salary from Company ABC at the end of15 years.
A=$45,500(1+8%/1)1times15A = \$45,500 (1 +8\%/1)^{1 \\times15}

STEP 4

Convert the percentage to a decimal value.
8%=0.088\% =0.08A=$45,500(1+0.08)15A = \$45,500 (1 +0.08)^{15}

STEP 5

Calculate the salary from Company ABC at the end of15 years.

STEP 6

Next, we need to calculate the salary from Company XYZ at the end of15 years. We can use the same formula for compound interest.

STEP 7

Now, plug in the given values for the starting salary, annual raise, and number of years to calculate the salary from Company XYZ at the end of15 years.
A=$62,000(1+3%/1)1times15A = \$62,000 (1 +3\%/1)^{1 \\times15}

STEP 8

Convert the percentage to a decimal value.
3%=0.033\% =0.03A=$62,000(1+0.03)15A = \$62,000 (1 +0.03)^{15}

STEP 9

Calculate the salary from Company XYZ at the end of15 years.

STEP 10

Now that we have the salaries from both companies at the end of15 years, we can compare them to see which one is higher.

STEP 11

If the salary from Company ABC is higher than the salary from Company XYZ, then Shannon would be making more at Company ABC. If the salary from Company XYZ is higher than the salary from Company ABC, then Shannon would be making more at Company XYZ.

STEP 12

To find out how much more Shannon would be making at the company with the higher salary, subtract the salary from the other company from the higher salary.

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