$1,000 is invested at a rate of 3.25%, compounded annually. Identify the compound interest function that models the situation. Then find the balance after 8 years.

The compounded interest function that models the situation is: [tex]A=P(1+ \frac{r}{n} )^{nt}[/tex]
where
[tex]A[/tex] is the final amount of money after [tex]t[/tex] years.
[tex]P[/tex] is the initial investment.
[tex]r[/tex] is the interest rate in decimal form.
[tex]n[/tex] is the number of times the interest is compounded per year.
[tex]t[/tex] is the time in years.

We know for our problem that [tex]P=1000[/tex] and [tex]t=8[/tex]. To convert the interest rate to decimal form, we are going to divide the rate by 100%:
[tex]r= \frac{3.25}{100} [/tex]
[tex]r=0.0325[/tex]
We also know that the interest is compounded anally, so it is compounded 1 time per year; therefore, [tex]n=1[/tex].
Lets replace the values in our formula to find the final amount after 8 years: 
[tex]A=P(1+ \frac{r}{n} )^{nt}[/tex]
[tex]A=1000(1+ \frac{0.0325}{1} )^{(1)(8)}[/tex]
[tex]A=1000(1+ 0.0325 )^{8}[/tex]
[tex]A=1291.58[/tex]

We can conclude that since we are dealing with compound interest we must use the function [tex]A=P(1+ \frac{r}{n} )^{nt}[/tex]. Also, after 8 years the balance in the account will be $1291.58