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? Round your answer to the nearest cent.

1) a20 = $
2) S20 = $

Question

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? Round your answer to the nearest cent.

1) a20 = $
2) S20 = $

rea201 · Answer

So for the first question we would make the equation. a20=32,000 x 1.05^(n-1). Because this is how to find the amount he made in a certain year. So, in year 20, he earned 32,000 x 1.05^19.

rea201 · Answer

For the second we need to find the sum of the geometric series. We will use the following formula. $$S_{20}=a\left( \frac{ 1-r^n }{ 1-r } \right)$$ Do you know what a is?