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.
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First, apply the 0.9% raise 4 times: Each time you get a raise of 0.9%, your new salary becomes:
After 4 raises of 0.9%, your salary becomes:
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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:
After 7 raises of 1.8%, your salary becomes:
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:
- How would the final salary change if the raises were applied in reverse order?
- What would be the salary after just the 4 raises of 0.9%?
- How much more would you earn annually after 5 years if your starting raise was 1.8% instead of 0.9%?
- What is the total percentage increase in salary after all the raises?
- 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
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