The forward rate f(t1,t2) of a bond, is the implicit interest rate in a future period between time t1 and t2. For example, assuming continuous time returns, if the discount rate from period 0 to t1 is: exp(-r t1), and from period 0 to t2 (greater than t1) is: exp(-r t2), then the forward rate f from t1 to t2 maintains the following no arbitrage relationship: exp(-r t1) exp(-f (t2-t1) = exp(-r t2)). Suppose we observe the prices of a 11-year zero-coupon bond (with a face value of $90.35), where P(t1,t2) means the price of the bond between t1 and t2, and a year 4-to-11 forward rate as follows:P(0,11) = $85.3536450000 and f(4,11) = 0.6175953186%. Calculate the price of a 4-year zero-coupon, with face value $90.42: