Question

Consider a 2-year Treasury bond with a face value of $100 and that pays coupons at a rate of 6% semiannually. What is the price of the bond given the following Treasury zero rates?

Maturity (years) Zero rates

0.5 3.0%

1.0 3.3%

1.5 3.6%

2.0 3.9%

a) $97.93

b) $99.97

c) $103.97

d) $108.93

Answer 1

NOTE: Please note that all zero rates provided are on an annualized basis and need to be divided by two for a 6-month period.

Face Value = $ 100, Coupon Rate = 6 % per annum payable semi-annually

Semi-Annual Coupon Payment = 0.06 x 100 x 0.5 = $ 3

0.5 year discount rate = (3/2) = 1.5 %, 1 year discount rate = (3.3/2) = 1.65 %, 1.5 year discount rate = (3.6/2) = 1.8 % and 2 year discount rate = (3.9/2) = 1.95 %

Therefore, Current Bond Price = 3 / (1.015) + 3 / (1.0165)^(2) + 3 / (1.018)^(3) + 103 / (1.0195)^(4) = $ 104.046 ~ $ 103.97

Hence, tne cprrect option is (c)