Question

Find the final hourly wage if a $15.00 starting wage is increased by 5% each year for 7 years. The final hourly wage is $. Round your answer to the nearest cent.

Answer 1

An increase of 5% means we will take 5% of the current value and add it to the current value.

This is the same as taking 105% of the current value. Since 105% is the same as 1.05, the 5% increase is the same as multiplying the current value by 1.05.

So, after 1 year, the new hourly wage will be 15 times 1.05:

`15\cdot1.05=15.75`

After the second year, we will apply this again, but now over the current value, which is 15.75. So we will multiply 15.75 by 1.05.

This is the same as multiplying the initial value by 1.05 twice:

`15\cdot1.05\cdot1.05=15\cdot(1.05)^2`

So, if we want the value after 7 year, it will be the same as multiplying 15 by 1.05 7 times:

`15\cdot(1.05)^7`

So, the value after 7 year will be:

`V=15\cdot(1.05)^7=15\cdot1.407100\ldots=21.106506\ldots\approx21.11`

The final value will be approximately $21.11.