Given that Andrew invests $9,000 at the end of each year for 20 years. The rate of interest Andrew gets is 8% annually.
Now we need to determine the final value of Andrew's investment at the end of the twentieth year on this ordinary annuity.
So we can use annuity formula which is :
[tex]S=R\left(\frac{\left(1+i\right)^n-1}{i}\right)[/tex]
Where R=annual payment = 9000
i= rate of interest = 8% = 0.08
t= number of years = 20
S= future value
Now plug those values into above formula.
[tex]S=9000\left(\frac{\left(1+0.08\right)^{20}-1}{0.08}\right)[/tex]
[tex]S=9000\left(\frac{\left(1.08\right)^{20}-1}{0.08}\right)[/tex]
[tex]S=9000\left(\frac{4.66095714385-1}{0.08}\right)[/tex]
[tex]S=9000\left(\frac{3.66095714385}{0.08}\right)[/tex]
[tex]S=9000(45.7619642981)[/tex]
S=411857.678683
Hence final answer is approx $411858.
