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QuestionWhat will a union member's salary be in 9 years if it increases by 5%5\% annually from a current salary of \$87,300?

Studdy Solution

STEP 1

Assumptions1. The current salary is $87,300. The annual raise is5%
3. The raise is compounded annually4. We are looking for the salary after9 years

STEP 2

We can use the formula for compound interest to calculate the future salary. The formula isA=(1+r/n)ntA =(1 + r/n)^{nt}Where- A is the amount of money accumulated after n years, including interest. - is the principal amount (the initial amount of money). - r is the annual interest rate (in decimal form). - n is the number of times that interest is compounded per year. - t is the time the money is invested for in years.
In this case, the principal amount is the current salary, the rate r is the raise rate, n is1 (since the raise is compounded annually), and t is9 years.

STEP 3

First, we need to convert the raise rate from a percentage to a decimal.
5%=0.055\% =0.05

STEP 4

Now, we can plug in the values into the formula.
A=$87,300(1+0.05/1)1times9A = \$87,300(1 +0.05/1)^{1 \\times9}

STEP 5

implify the formula.
A=$87,300(1+0.05)9A = \$87,300(1 +0.05)^9

STEP 6

Calculate the future salary.
A=$87,300(1.05)9A = \$87,300(1.05)^9

STEP 7

Calculate the future salary.
A=$87,300times1.5513282166A = \$87,300 \\times1.5513282166

STEP 8

Calculate the future salary.
A=$135,341.06A = \$135,341.06The union member's salary will be approximately $135,341.06 in years.

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