Question

if your starting salary were 35000 and you received a 6% 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?

Answer 1

$898538

Explanation:

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Answer 2

You will earn $898,538.48 over the first 16 years.

Explanation:

Your starting salary were $35000 and you received a 6% increase at the end of every year.

So at the end of first year your salary would be,

`=35000+35000* (6)/(100)`

`=35000+35000* 0.06`

`=35000(1+0.06)`

`=35000(1.06)`

Then at the end of second year your salary would be,

`=(35000(1.06))+(35000(1.06))* 0.06`

`=35000(1.06)(1+0.06)`

`=35000(1.06)(1.06)`

`=35000(1.06)^2`

From this it is evident that this series is in Geometric Series, with initial term as 35000 and common ratio as 1.06

The sum of first n terms in a GP is,

`S_n=(a_1(1-r^n))/(1-r)`

So, putting the values,

`S_(16)=(35000(1-(1.06)^(16)))/(1-1.06)`

`=\$898,538.48`