Start by writing out the equation:

\(2000\)\((1+\)\(\frac{i}{200}\)\()^{10}\)\(=6000\)

Now divide both sides by 2000:

\((1+\)\(\frac{i}{200}\)\()^{10}\)\(=3\)

We want to manipulate the equation in order to get the exponent to become 30, which represents 15 years of investment semi-annually.

To do this, cube both sides of the equation:

\([\)\((1+\)\(\frac{i}{200}\)\()^{10}\)\(]^3\)\(=(3)^3\)

\((1+\)\(\frac{i}{200}\)\()^{30}\)\(=27\)

Now multiply both sides by 2000 again:

\(2000\)\((1+\)\(\frac{i}{200}\)\()^{30}\)\(=54000\)

We have that, after 15 years, the $2000 investment compounded semiannually will be $54000.

Therefore, the answer is C