We need to find the amount A in the account after a deposit P = 2000 dollars, with an interest rate r = 6% = 0.06 compounded quarterly (n = 4), stays there for t = 1 year.
The formula relating those quantities is:
[tex]A=P\left(1+\frac{r}{n}\right)^{nt}[/tex]Then, using the given information, we obtain the amount A, in dollars:
[tex]\begin{gathered} A=2000\cdot\left(1+\frac{0.06}{4}\right)^{4\cdot1} \\ \\ A=2000\cdot\left(1.015\right)^4 \\ \\ A\cong2122.73 \end{gathered}[/tex]Answer: $2122.73.
