that was a really poor explanation for the spot and forward rate.

the fact that CFAI does such a poor job explaning this fundamental theory is disappointing.

below is a paraphrase from a financial math book i used:

spot rate of interest is the annualized effective rate of interest from time 0 to time t, where time 0 is the present time. you can have a spot rate of interest over a year (from time 0 to time 1), over 5 years (from time 0 to time 5), etc. The spot rate is determined at time 0.

Forward rate of interest is the rate of interest for a single period in the future (from time t - 1 to time t). For example, the rate of interest from time 0 to time 1, from 1 to time 2, from time 2 to time 3, from time 3 to time 4, etc. this rate of interest is determined at time 0. Unlike spot rates, forward rates only apply for a single period.

also note that when t = 1, spot rate and forward rate are identical.

for example, you could have a spot rate of interest over 2 years to equal 4%, while the forward rate from time 0 to time 1 is 5% and the forward rate from time 1 to time 2 equal 3% (the value 4% for the spot rate is only approximate. see below)

one important relation between spot rate of interest and forward rate of interest is the following:

let F(T - 1, T) be the forward rate of interest from time T - 1 to T.

and S(0, T) be the spot rate of interest, that is, the annualized effective rate of interest over T periods. then:

(1 + S(0, T) )^T = (1 + F(0, 1) ) x (1 + F(1, 2) ) x … x (1 + F(T - 1, T) )

also,

1 + F(T - 1 , T) = {(1 + S(0, T) ) ^T } / { (1 + S(0, T - 1)^ (T - 1) }

maybe it is easier to see the difference with a time diagram (that is how the book showed the difference)

draw a time diagram and draw a line on top from time 0 to time T. that is your spot rate. now draw a line from time 0 to time 1, and another line from time 1 to time 2, etc. these are your forward rates.