Question

2) Suppose the one year spot rate is 3% and two year spot rate is 4%. a) What is the price of a two year ZCB? b) What is the price of a one year ZCB today? c) What do I expect the price of a one year ZCB to be, one year from now?

Answer 1

a.price of a two year ZCB = par value / (1+interest rate)^n

here,

Par value = $1000....(default par value)

r =4% =>0.04

n = 2.

=>price = $1000/ (1.04)^2

=>$924.56.

b.price of one year ZCB today:

=> par value / (1+ interest rate)^n

here,

interest rate = 3%

n=1.

=>$1000/(1.03)^1

=>$970.87.

c.required interest rate will be the average of current interest rates for two years

=> (3%+4%)/2

=>3.5%.

price of one year bond after one year = par value / (1+interest rate)^1

=>$1,000 / (1.035)^1

=>$966.18.