Question

Suppose that a two-year bond with a principal of $100 provides coupons at the rate of 6% per annum semiannually. Suppose that the zero-rates are

Maturity (years)	Zero Rate (%)
0.5	5.0
1.0	5.8
1.5	6.4
2.0	6.8

What is the current theoretical price of the bond?

- please use formulas and explain step by step

Answer 1

Given about a bond,

Face value/principal = $100

Coupon rate = 6% paid semiannually,

=> semiannual coupon payment = (6%/2) of 100 = $3

So, price of the bond using zero rates is calculated as

Price = C/(1 + r0.5/2) + C/(1 + r1/2)^2 + C/(1+r1.5/2)^3 + (C+FV)/(1+r2/2)^4

=> Price = 3/(1+0.05/2) + 3/(1+0.058/2)^2 + 3/(1+0.064/2)^3 + 103/(1+0.068/2)^4 = $98.60

So, current theoritical price of the bond is $98.60