Question

Alex gets a 3% raise at the end of every year he works for a company. At the end of his fourth year, he is earning $50,648. Find his starting salary, to the nearest dollar.

Answer 1

Alex's starting salary can be calculated by reversing the compounded 3% annual raises given over four years. By dividing his fourth-year salary of $50,648 by (1.03)^4, we find that his approximate starting salary was $45,000.

Step-by-step explanation:

To determine Alex's starting salary, we have to reverse the process of annual 3% raises over four years. The salary at the end of the fourth year is $50,648, which is after four cumulative increments. To reverse this, we use the formula for the original amount before a percentage increase: Original Amount = Final Amount / (1 + Raise).

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• First, calculate the raise factor: 3% as a decimal is 0.03, so 1 + 0.03 = 1.03.
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• Second, reverse the raises for each of the four years. Notice that we compound the raise by raising the factor to the power of four because the raises happen each year.
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• So, we have: Starting Salary = $50,648 / (1.03)^4
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• Calculating this, we get: Starting Salary = $50,648 / (1.1255) approximately.
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• The starting salary comes out to be approximately $45,000.

This method systematically reverses the compounded annual growth rate (CAGR) of Alex's salary to establish his starting salary.

Answer 2

To find Alex's starting salary, work backwards from his salary at the end of the fourth year. Divide each year's salary by 1.03 to find the previous year's salary until you reach the starting salary.

Step-by-step explanation:

To find Alex's starting salary, let's work backwards from his salary at the end of the fourth year. We know that he gets a 3% raise at the end of every year, so we can calculate the salary for each year. Starting from the fourth year salary ($50,648), we divide it by 1.03 (1 + 0.03) to find the salary at the end of the third year. Then we repeat the process to find the salary at the end of the second year, first year, and finally the starting salary.

Year 4 salary: $50,648

Year 3 salary: $50,648 / 1.03 = $49,130.10

Year 2 salary: $49,130.10 / 1.03 = $47,680.49

Year 1 salary: $47,680.49 / 1.03 = $46,293.08

Starting salary: $46,293.08 / 1.03 = $44,907.66 (rounded to nearest dollar)