Question

You are given the following information with respect to a bond:

par amount: 1000 / term to maturity 3 years / annual coupon rate 6% payable annually

You are also given that the one, two, and three year annual spot interest rates are 7%, 8%, and 9% respectively.

1). Calculate the value of the bond.

2). Calculate the annual effective yield rate for the bond if the bond is sold at a price equal to its value.

Answer 1

Solution:-

1) Annual coupon amount = 1000 * 6%

                                           = 60

Value of Bond = 60*(P/A,7%,1)+60*(P/A,8%,2)+60*(P/A,9%,3)+1000*(P/A,9%,3)

                          =60*.9346 + 60*.8573 + 60*.7722+1000*.7722

                          =56.076+51.438+46.332+772.2

                          =926.046

Value of Bond = $926.05

2) Future value = 1000, Present Value = 926.02

Let effective yield r% then,

926.05= 60/(1+r) + 60/(1+r)^2 + 1060/(1+r)^3

By hit and trial Method r = 8.9%