Question

the three-year zero rate is 5% and the 1-year forward rate after year three is 6%. what is the four-year rate? assume continuous compounding

Answer 1

e^{-(4-year rate * t)} = e^{-(3-year rate * t)} * e^{-(1-year forward rate,3 years from now * t)}

e^{-(4-year rate * 4)} = e^{-(0.05 * 3)} * e^{-(0.06 * 1)}

e^{-(4-year rate * 4)} = 0.8607 * 0.9418

e^{-(4-year rate * 4)} = 0.8106

-(4-year rate * 4) * log(e)= log(0.8106)

-(4-year rate * 4) * 1 = -0.21

4-year rate = 0.21 / 4 = 0.0525, or 5.25%