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If your starting salary is $40,000 and you receive a 3% increase at the end of every year, what is the total amount, in dollars, you will earn over the first 16 years that you work?Round your answer to the nearest whole dollar, and express your answer without using commas.Answer here

Question

If your starting salary is $40,000 and you receive a 3% increase at the end of every year, what is the total amount, in dollars, you will earn over the first 16 years that you work?Round your answer to the nearest whole dollar, and express your answer without using commas.Answer here

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Solution

To solve this problem, we need to use the formula for the sum of a geometric series. The formula is:

S = a * (1 - r^n) / (1 - r)

where:

  • S is the sum of the series
  • a is the first term in the series
  • r is the common ratio
  • n is the number of terms

In this case:

  • a is the starting salary, which is $40,000
  • r is the annual increase, which is 1 + 3% = 1.03
  • n is the number of years, which is 16

Substituting these values into the formula, we get:

S = 40000 * (1 - 1.03^16) / (1 - 1.03)

Calculating this gives:

S = 40000 * (1 - 1.03^16) / -0.03

S = 40000 * -0.593305 / -0.03

S = 791,175.83

Rounding to the nearest whole dollar gives 791176.

So, the total amount you will earn over the first 16 years that you work is $791,176.

This problem has been solved

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