In order to calculate the final value after 7 years, we can use the formula below:
[tex]A=P\cdot(1+\frac{i}{n})^{nt}_{}[/tex]
Where A is the final amount after t years, P is the principal (initial value), i is the annual interest rate and n is how many times the interest is compounded in a year.
So, for P = 2000, i = 0.195, t = 7 and n = 2, we have:
[tex]\begin{gathered} A=2000(1+\frac{0.195}{2})^{2\cdot7} \\ A=2000(1.0975)^{14} \\ A=7356.88 \end{gathered}[/tex]
Therefore the final amount is $7356.88.
