Math Problem Statement

Suppose your annual starting salary is $59,942. After working for a few years, you start to get yearly raises. If you get a 0.9% raise a total of 4 times and then a 1.8% raise a total of 7 times, what is your salary after all the raises?

Solution

To find the final salary after receiving a series of raises, we'll apply the following steps:

Initial salary: $59,942.

  1. First, apply the 0.9% raise 4 times: Each time you get a raise of 0.9%, your new salary becomes:

    New Salary=Current Salary×(1+0.009)\text{New Salary} = \text{Current Salary} \times (1 + 0.009) After 4 raises of 0.9%, your salary becomes:

    S1=59,942×(1+0.009)4S_1 = 59,942 \times (1 + 0.009)^4

  2. Next, apply the 1.8% raise 7 times: After the 0.9% raises, we apply a 1.8% raise. The formula for each raise becomes:

    New Salary=Current Salary×(1+0.018)\text{New Salary} = \text{Current Salary} \times (1 + 0.018) After 7 raises of 1.8%, your salary becomes:

    Sfinal=S1×(1+0.018)7S_{\text{final}} = S_1 \times (1 + 0.018)^7

Let's calculate the final salary.After applying 4 raises of 0.9% and 7 raises of 1.8%, your final salary would be approximately $70,393.14.

Would you like further details or have any questions?

Here are five related questions:

  1. How would the final salary change if the raises were applied in reverse order?
  2. What would be the salary after just the 4 raises of 0.9%?
  3. How much more would you earn annually after 5 years if your starting raise was 1.8% instead of 0.9%?
  4. What is the total percentage increase in salary after all the raises?
  5. How long would it take to double your salary if you continue receiving 1.8% raises?

Tip: Compound interest (or compound growth) is powerful over time, even small percentages can make a big difference with repeated application.

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Math Problem Analysis

Mathematical Concepts

Compound Interest
Exponential Growth

Formulas

New Salary = Current Salary × (1 + Raise Percentage)^Number of Raises
S_final = S_initial × (1 + 0.009)^4 × (1 + 0.018)^7

Theorems

Compound Growth Theorem

Suitable Grade Level

Grades 9-12