Answer:
$2186.17
Explanation:
The amount in the account after 2 years can be calculated using the following equation:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where P is the initial amount, r is the interest rate, n is the number of times the interest is compound per year and t is the number of years.
The interest rate is 4 1/2 % which is equivalent to 4.5% or 0.045 because:
[tex]4\frac{1}{2}=4+\frac{1}{2}=4+0.5=4.5[/tex]Then, replacing P by $2,000, r by 0.045, n by 2, and t by 2 years, we get:
[tex]\begin{gathered} A=2000(1+\frac{0.045}{2})^{2\cdot2} \\ A=2000(1+\frac{0.045}{2})^4 \\ A=2000(1+0.0225)^4 \\ A=2000(1.0225)^4 \\ A=2000(1.093) \\ A=2186.17 \end{gathered}[/tex]Therefore, after 2 years there will be $2186.17 in the account.
