The formula of the present value of annuity due:
[tex]PV=C*[\frac{1-(1+i)^{-n}}{i}]*(1+i)[/tex]
For your case:
C = $3000
i = 12% / 100 = 0.12
n = 3 * 2 = 6 (semiannually for 3 years means 6 payments)
So, the solution is:
[tex]PV=3000*[\frac{1-(1+0.12)^{-6}}{0.12}]*(1+0.12)=3000*[\frac{1-0.5066}{0.12}]*1.12=[/tex]
[tex]=3000*[\frac{1-0.5066}{0.12}]*1.12=3000*4.1114*1.12=13814.32[/tex]
