The compound interest formula is given by
[tex]A=P(1+\frac{r}{n})^{n\times t}[/tex]where A is the resulting amount after t years, P is the present value (or principal amount) , r is the annual interest rate and n is the number of compounding periods per year.
From the given information, we have that
[tex]\begin{gathered} P=1000 \\ r=0.04 \\ n=4\text{ (quaterly=4 times per year)} \\ t=12\text{ years} \end{gathered}[/tex]By substituting these values into the formula, we have
[tex]A=1000(1+\frac{0.04}{4})^{4\times12}[/tex]which gives
[tex]\begin{gathered} A=1000(1.01)^{48} \\ A=1000(1.6122) \\ A=1612.226 \end{gathered}[/tex]Therefore, by rounding to the nearest thousandth, the answer is $1612.23, which corresponds to the last option.
