To solve this, we are going to use the compound interest formula: [tex]A=P(1+ \frac{r}{n} )^{nt}[/tex]
where
[tex]A[/tex] is the final amount after [tex]t[/tex] years.
[tex]P[/tex] is the initial amount.
[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 from our problem that Jesse's decides to invest his income tax refund of $2300, so [tex]P=2300[/tex]. We also know that the number of years is 3, so [tex]t=3[/tex]. Since the interest was compounded semi-annually, it was compounded 2 times per year; therefore, [tex]n=2[/tex]. Now, to convert the interest rate to decimal form, we are going to divide the rate by 100%
[tex]r= \frac{5.5}{100} [/tex]
[tex]r=0.055[/tex]
Now that we have all the values we need, lest replace in our formula:
[tex]A=P(1+ \frac{r}{n} )^{nt}[/tex]
[tex]A=2300(1+ \frac{0.055}{2})^{(2)(3)} [/tex]
[tex]A=2706.57[/tex]
We can conclude that the value of the CD after 3 years of yielding an interest of 5.5% compounded semi-annually is 2706.57