Answer:
$5,591.46
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 2.5% into a decimal:
2.5% -> [tex]\frac{2.5}{100}[/tex] -> 0.025
Since the interest is compounded semiannually, we will use 2 for n. Lets plug in the values now:
[tex]A=5,000(1+\frac{0.025}{2})^{2(4.5)}[/tex]
[tex]A=5,591.46[/tex]
The amount in the account after 4.5 years is $5,591.46
