Answer
$\$ 10,538.96$
Work Step by Step
A sinking fund is an account earning compound interest into which you make periodic deposits.
Here, $\\\\$
r$=0.0525 \ \ \ \ ...$annual rate$, \\\\$
m$=2 \ \ \ \ $ ...compounding periods per year, $\\\\$
i = r /m$=\displaystyle \frac{0.0525}{2} \ \ \ \ ...$ interest rate per compounding period. $\\\\$
If you make a payment of PMT$=2000$ dollars $\\\\$
at the end of each period, then the future value $\\\\$
after $t=2.5$ years, $\\\\$
or, $n = mt =2(2.5)=5 \ \ \ \ $ periods, $\\\\$
will be$\\\\$
$FV=PMT\displaystyle \cdot\frac{(1+i)^{n}-1}{i}\\\\$
$=2000\displaystyle \cdot\frac{(1+\frac{0.0525}{2})^{5}-1}{\frac{0.0525}{2}}\approx$10538.9630785