Given:
Annual interest rate = r%
Growth factor : x = 1 + r
The below function gives the amount in the account after 4 years when the growth factor is x .
[tex]A(x)=800x^4+350x^3+500x^2+600x[/tex]
To find:
The total amount in the account if the interest rate for the account is 3% each year and initial amount.
Solution:
Rate of interest = 3% = 0.03
Growth factor : x = 1 + 0.03 = 1.03
We have,
[tex]A(x)=800x^4+350x^3+500x^2+600x[/tex]
Substitute x=1.03 in the given function, to find the total amount in the account if the interest rate for the account is 3% each year.
[tex]A(1.03)=800(1.03)^4+350(1.03)^3+500(1.03)^2+600(1.03)[/tex]
[tex]A(1.03)=800(1.12550881)+350(1.092727)+500(1.0609
)+618[/tex]
[tex]A(1.03)=900.407048+382.45445+530.45+618[/tex]
[tex]A(1.03)=2431.311498
[/tex]
[tex]A(1.03)\approx 2431.31
[/tex]
Therefore, the total amount in the account is 2431.31 if the interest rate for the account is 3% each year.
For initial amount the rate of interest is 0.
Growth factor : x = 1 + 0 = 1
Substitute x=0 in the given function to find the initial amount.
[tex]A(1)=800(1)^4+350(1)^3+500(1)^2+600(1)[/tex]
[tex]A(1)=800+350+500+600[/tex]
[tex]A(1)=2250[/tex]
Therefore, 2250 was put into the account at the beginning.
