Question

____ is the amount of a $3,000.00 annuity due at 12 percent compounded semiannually for 3 years

Answer 1

The formula of the present value of annuity due:
$PV=C*[\frac{1-(1+i)^{-n}}{i}]*(1+i)$

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:
$PV=3000*[\frac{1-(1+0.12)^{-6}}{0.12}]*(1+0.12)=3000*[\frac{1-0.5066}{0.12}]*1.12=$
$=3000*[\frac{1-0.5066}{0.12}]*1.12=3000*4.1114*1.12=13814.32$