#### Answer

Amount owed at the end of six years is $\$14,753.92$.

#### Work Step by Step

Find the total amount due using the formula $A=P\left(1+\dfrac{r}{n}\right)^{nt}$ where $P$=principal loan amount, $r=$annual interest rate, $t$=time in years, and $n$=number of compounding periods in a year
The given problem has:
$P=\$10,500$
$t=6$
$r=5.75\%$
$n=2$ (since compounded semi-annually)
Use the formula above to obtain:
$A=\$10,500\left(1+\dfrac{5.75\%}{2}\right)^{2(6)}
\\A=\$10,500\left(1+\dfrac{0.0575}{2}\right)^{2(6)}
\\A=\$14,753.92182
\\A\approx \$14,753.92$