Assume you have six different bonds: 

• B1 A two-year bond with a nominal rate of 2 % per annum

• B2 – A three-year bond with a nominal rate of 2.5 % per annum

• B3 – A five-year bond with a nominal rate of 3 % per annum

• B4 – An eight-year bond with a nominal rate of 4 % per annum

• B5 – A ten-year bond with a nominal rate of 4 % per annum

• B6 - A twenty-year bond with a nominal rate of 5 % per annum

Suppose a fund manager is committed to making annual payments of $25,000 for the next 20 years (an annuity) and they use a discount rate of 0.03 or 3 % pa.

(a) What is the Present Value of these payments?

(b) To fund these payments the fund manager must invest in the six bonds described in above . Assume she is trying to minimize transaction costs; use the figures in above  to write the equations that would need to be satisfied to immunize the annuity described in this question. 

Note that the fund manager is concerned that the application of these conditions could result in only one or two different types of bonds being held. As this is considered risky she introduces a diversification condition whereby she must hold a minimum of five of each of B1, B2, B3, B4, B5 and B6. This condition will also need to be considered in your equations.