Forward rate

The forward rate is the future yield on a bond. It is calculated using the yield curve. For example, the yield on a three-month Treasury bill six months from now is a forward rate. The forward rate is the future yield on a bond. It is calculated using the yield curve. For example, the yield on a three-month Treasury bill six months from now is a forward rate. To extract the forward rate, we need the zero-coupon yield curve. We are trying to find the future interest rate r 1 , 2 {displaystyle r_{1,2}} for time period ( t 1 , t 2 ) {displaystyle (t_{1},t_{2})} , t 1 {displaystyle t_{1}} and t 2 {displaystyle t_{2}} expressed in years, given the rate r 1 {displaystyle r_{1}} for time period ( 0 , t 1 ) {displaystyle (0,t_{1})} and rate r 2 {displaystyle r_{2}} for time period ( 0 , t 2 ) {displaystyle (0,t_{2})} . To do this, we use the property that the proceeds from investing at rate r 1 {displaystyle r_{1}} for time period ( 0 , t 1 ) {displaystyle (0,t_{1})} and then reinvesting those proceeds at rate r 1 , 2 {displaystyle r_{1,2}} for time period ( t 1 , t 2 ) {displaystyle (t_{1},t_{2})} is equal to the proceeds from investing at rate r 2 {displaystyle r_{2}} for time period ( 0 , t 2 ) {displaystyle (0,t_{2})} . r 1 , 2 {displaystyle r_{1,2}} depends on the rate calculation mode (simple, yearly compounded or continuously compounded), which yields three different results.