(b) A fund has liabilities of $2 million due in 7 years' time and $4 million due in 10 years' time. Two zero-coupon bonds with terms to maturity of 5 years and 12 years are available for investment purpose. Determine the required nominal dollar amounts of these two bonds such that the present values and the modified durations of assets and liabilities are matched at a constant effective interest rate of 8% per annum and verify that the convexity of the assets is larger than the convexity of the liabilities. (6 marks)