# Math Help - PV

1. ## PV

I am not sure if I titled this one correctly but here it is....

Fred purchased a farm with a down payment of $8,500 and forty-eight (48) semi-annual payments of$3,000. The first of these payments is to be made two (2) years after the date of purchase. What was the purchase price of the farm if the interest rate charged on the balance is 14% compounded semi-annually?

n 48
i 7
PMT 3,000 0
FV 0
PV ? = 41,191.42

n 3
i 7
FV 41,191.42
PV 33,624.47 + 8,500 = 42,124.47

I know this is the right answer but I am struggling to understand why the second N is 3 instead of 4? It has been explained but I am having a hard time grasping it.

Thanks in advance.

2. By using the formula for the PV of an ordinary annuity, you determined the PV of the 3k annuity as of a point that's six months prior to the first 3,000 payment. So then to bring it back to today, you had to discount that PV back another 3 six-month periods.