Answer:
You will earn $898,538.48 over the first 16 years.
Step-by-step 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,
[tex]=35000+35000\times \dfrac{6}{100}[/tex]
[tex]=35000+35000\times 0.06[/tex]
[tex]=35000(1+0.06)[/tex]
[tex]=35000(1.06)[/tex]
Then at the end of second year your salary would be,
[tex]=(35000(1.06))+(35000(1.06))\times 0.06[/tex]
[tex]=35000(1.06)(1+0.06)[/tex]
[tex]=35000(1.06)(1.06)[/tex]
[tex]=35000(1.06)^2[/tex]
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,
[tex]S_n=\dfrac{a_1(1-r^n)}{1-r}[/tex]
So, putting the values,
[tex]S_{16}=\dfrac{35000(1-(1.06)^{16})}{1-1.06}[/tex]
[tex]=\$898,538.48[/tex]
