Consider that the amount is given by,
[tex]A=P(1+r)^n[/tex]Here, 'P' is the principal, 'n' is the number of compounding periods, 'r' is the effective rate of interest per period.
Given that compounding is done semiannually i.e. twice a year, so the number of periods in 12 years will be 24,
[tex]n=2\times12=24[/tex]The effective rate of interest is given by,
[tex]r=\frac{7}{2\times100}=0.035[/tex]Substitute the values and solve for the amount as follows,
[tex]\begin{gathered} A=14000(1+0.035)^{24} \\ A=14000\times2.28 \\ A=31966.60 \end{gathered}[/tex]Thus, the required amount will be $31966.60
Therefore, option J is the correct choice.
