Question

Every six months, Jacinda deposits $475 into an interest-bearing account to save for her children's tuition. The interest rate on the account is 7.1% compounding semiannually. What is the present value of the investment if Jacinda's children leave for college in 9 years?

$4,743.77
$5,080.58
$6,460.70
$6,239.21

Answer 1

The future value annuity is given by:
FV=(1+r)*p{[(1+r)^n-1]/r}
our value will be:
FV=(1+0.071/2)*450{[(1+0.071/2)^(9*2)-1]/0.071/2}
FV=11,468.337

The present value of the annuity will be:
FV=PV(1+r)^n
11,468.337=PV(1+0.071)^9
solving for PV we get
PV=6185.791

Answer: PV=$6185.791

Answer is D]