Up until now, i thought that the PV had to be the opposite sign as whatever the PMT and FV was.
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PV = 500,000; N = 12; PMT = 12,700 ; FV = –2,000,000; CPT → I/Y = 11%.
WOAH.
You’re thinking of situations where you make an investment and get cash flows from that investment. Forget about your PV is opposite of PMT and FV rule. It can get you in a lot of trouble!
a better convention - which followed consistently helps
inflow = positive
outflow = negative
I tell my candidates to pick one viewpoint and stick with it.
If you choose the viewpoint of Smith, then PV is negative (he contributes it to his account), PMT is negative (ditto), and FV is positive (he withdraws the money).
If you choose the viewpoint of Smith’s account, then PV is positive (Smith gives the account $500,000), PMT is positive (ditto), and FV is negative (the account gives Smith his money).
It’s better to think whether the cash flows are coming in or going out, rather than memorizing some arbitrary relationship (the sign on PMT is whatever).
Great advice.
The reason you thought the PV is negative is because you always computed the cash flow today that would negate all the future cash flows with a certain rate of return.
in this case the person pays an amount today (PV) and will pay again regularly (PMT) in order to receive a cashhflow at the end (FV). To be self financed, the whole thing needs to be worth 0 with a certain rate of return.