5. An investor has to pay a lump sum of $1,000,000 at the end of 10 years from now and an annuity of $100,000 per annum for 30 years. The first annuity payment will be made one year from now. The investor currently holds an amount of cash equal to the present value of these two liabilities valued at an effective rate of interest of 6% per annum. The investor wishes to immunize his fund against small changes in the rate of interest by investing the cash in two zero coupon bonds, namely Bond A and Bond B. The market prices of both bonds are calculated at an effective rate of interest of 6% per annum. The investor has decided to invest an amount in Bond A so that he will receive an amount of $700,000 at maturity in one year's time. The remainder of the cash is invested in Bond B. Determine the term needed and the amount payable at maturity for Bond B so that his fund can be immunized