A 5% raise each year for 20 years

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Question from marie, a student:

In his first year, a math teacher earned 32,000. Each successive year, he earned a 5% raise. How much did he earn in his 20th year? What were his total earnings over the 20-year period

Hi Marie.

In year one, he earned 32,000.
In year two, he earned 32,000 x 1.05 (that's 105% of year one)
In year three, he earned (32,000 x 1.05) x 1.05 = 32,000 x 1.05² (that's 105% of year two).
...
In year n, he earned 32,000 x 1.05^n-1.
...
In year 20, he earned 32,000 x 1.05¹⁹.

As you can see, each year is 1.05 times the last. This is a geometric series.

For part two of the question, look at your textbook or study notes for how to find the sum of a geometric series. The ratio between successive terms is 1.05, the first term is 32,000 and there are 20 terms in all.

Cheers,
Stephen La Rocque.

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