Question

Consider the following three zero-coupon (discount) bonds: Face Value Market Pricee Time to Maturity Bond $924.64 One year $1,000 1e $841.53 Two years $1,000 2e $744.59 Three years $1,000 3 a) Calculate the one-, two-, and three-year spot rates. (3 marks) b) Calculate the forward rate over the second year and the forward rate over the third year. (2 marks)

Answer 1

Ans:

a) One, Two and Three year spot rate:

r = (1000/924.64) - 1 = 0.0815 i.e. 8.15%

So that

Spot rate are

1 bond = $ 924.64

2 bond = 1000/(1.0815)² = $ 854.96

3 bond = 1000/(1.0815)³ = $ 790.53

b) Forward rate

for the 2nd year = 9.87%

for the 3rd year = 13%