Using compound interest, it is found that it will take 11.28 years for the the account to grow to $4500.
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
A(t) is the amount of money after t years.
P is the principal(the initial sum of money).
r is the interest rate(as a decimal value).
n is the number of times that interest is compounded per year.
t is the time in years for which the money is invested or borrowed.
In this problem:
- $3000 is placed in the account, thus [tex]P = 3000[/tex].
- Interest rate of 3.6%, thus [tex]r = 0.036[/tex].
- Monthly compounding, thus [tex]n = 12[/tex].
We have to solve for t when [tex]A(t) = 4500[/tex], thus:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]4500 = 3000(1 + \frac{0.036}{12})^{12t}[/tex]
[tex](1.003)^{12t} = 1.5[/tex]
[tex]\log{(1.003)^{12t}} = \log{1.5}[/tex]
[tex]12t\log{1.003} = \log{1.5}[/tex]
[tex]t = \frac{\log{1.5}}{12\log{1.003}}[/tex]
[tex]t = 11.28[/tex]
It will take 11.28 years for the the account to grow to $4500.
A similar problem is given at https://brainly.com/question/24507395
