A pension fund discovers that it must make additional annual pension payments of $1m in years 6 through 10. The current interest rate is 5% and the term structure is flat. The pension fund seeks to hedge the additional liability by investing in two bond portfolios A and B with durations 5 and 15, respectively. The fund must also ensure that the investment in A and B matches the value of the additional pension payments. How much should be invested in portfolios A and B? (9 marks)