The compounding interest formula is :
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where A = future amount after t years
P = Initial amount
r = rate of interest
n = number of compounding
From the problem :
P = 5000
r = 7.2% or 0.072
n = 12 (compounded monthly)
Using the formula above :
[tex]\begin{gathered} A=5000(1+\frac{0.072}{12})^{12t} \\ A=5000(1.006)^{12t} \end{gathered}[/tex]The function will be :
[tex]A(t)=5000(1.006)^{12t}[/tex]Additional Information :
The formula was derived from :
[tex]A=P+I[/tex]where P = principal amoutn
A = future amount
I = Interest
The formula for interest is :
[tex]I=P(\frac{r}{n})[/tex]Substitute it to the formula above :
[tex]\begin{gathered} A=P+I \\ A=P+P(\frac{r}{n}) \end{gathered}[/tex]Factor out P :
[tex]A=P(1+\frac{r}{n})[/tex]