Question

$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.

Answer 1

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

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

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