Answer:
$6,066.82
Step-by-step explanation:
Lets use the compound interest formula provided to solve this:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
P = initial balance
r = interest rate (decimal)
n = number of times compounded annually
t = time
First, change 10% into a decimal:
10% -> [tex]\frac{10}{100}[/tex] -> 0.10
Since the interest is compounded monthly, we will use 12 for n. Lets plug in the values now:
[tex]A=4,500(1+\frac{0.10}{12})^{12(3)}[/tex]
[tex]A=6,066.82[/tex]
The balance after 3 years will be $6,066.82