how do i answer this question?  what is the formula?

suppose the current yeilds on treasury securities are:
one-year(1.05%), two-year(1.3%), three-year(1.4%), and
four-year(1.5%).  What is the implied forward interest rate two years
from not to four years from now?

Hey fizzleclizze

This is how I see it.

The forward rate R for year n can be found with the spot rates r using
the following formula:

R(n) = r(n) * n - r(n-1) * (n-1)
       -------------------------
             (n) - (n-1)

So, for year 2

R(2) = (0.013 * 2 - 0.0105 * 1) / 1
     = 0.0155
which is 1.55%

I guess you should be able to figure out the rest. :)

Suppose you invest 100 today for two years in one security and another
100 for four years in another security

after two years first one gives you get 100*(1.013)^2=102.617
after four years second one gives you 100*(1.015)^4 =106.136

So investing 102.617 after two years will implicitly give 106.136 after four years

so forward interest after two years for two years rate is 
= (106.136/102.612)^1/2-1

general formula for m years forward interest rate that will prevail n
years from now if r(n) and r(m+n) are present interest rates for n
years and n+m years securities from now is given by

==   (((1+r(m+n))^(m+n)/(1+r(n))^n)^1/m) - 1