Value (long) = St/(1+B)T-t – F0/(1+P)T-t
Why we have to divide the spot price at time t by one plus the base currency interest rate from maturity to time t?
If you settle the forward today, you won’t settle it for the contracted amount of the base currency; you’ll settle it for the present value of the contracted amount of the base currency, which is the contracted amount divided by the base currency risk-free rate for the remaining time.
You’re not actually discounting the spot rate; you’re discounting the amount of the base currency which you will multiply by the spot rate.
I wrote an article that explains this in more detail: http://www.financialexamhelp123.com/valuing-a-currency-forward-whence-came-that-formula/.
(Full disclosure: as of 4/25/16 there is a charge to read the articles on my website. You can get an idea of the quality of the articles by looking at the free samples here: http://www.financialexamhelp123.com/sample-articles/.)