We, what, if you know all the spot rates we can

compute out what the forwards rates are going to be, and

the way to use them is to think about two different

ways that you can go from year 0 to year V.

One possibility is go, is going to be to lend $1 up to time V.

In which case, this $1 lent for V years at time

0 is going to give, going to be worth 1 plus SV to the power V.

The other possibility is to lend that dollar for U years and then

contract it right away at time T equal to 0 to lend it for another V minus U years.

So it's

important to remember what we're doing here

in the second level option is that we're

going to lend the dollar for U years and right at time T equal to 0

I'm going to construct another contract which is going to allow me to lend at

whatever amount of money that I have at time U for another V minus U years.

So my initial dollar is going to be worth 1 plus SU to the power U.

This entire amount is now going

to be lent at the forward rate.

So if I lend it, I get 1 plus FUV to the power V minus U at time V.