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*[(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*[(1-(1+0.12)^(-6))/(0.12)]*(1+0.12)=3000*[(1-0.5066)/(0.12)]*1.12=`

`=3000*[(1-0.5066)/(0.12)]*1.12=3000*4.1114*1.12=13814.32`