The formula for compound interest is:
[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]
Where:
A is the amount in the account after t years.
P is the amount initially invested.
r is the rate of compounding per year, in decimal.
n is the number of times compounded in a year.
t is the number of years since the initial investment.
The problem tells us:
The initial amount is P = 12000
The annual compounding rate is 4.5%, to convert to decimal, we divide by 100:
[tex]r=\frac{4.5}{100}=0.045[/tex]
Since the amount is compounded daily, it's compounded 365 times a year. Thus, n = 365
Now we can write:
[tex]A(t)=12000(1+\frac{0.045}{365})^{365t}[/tex]
Which is option 3
Thus, the correct answer is option 3:
[tex]A(t)=12000(1+\frac{0.045}{365})^{365t}[/tex]
