An insurance company must make a payment of $500,000 in exactly five years. In order to provide for this obligation, their CFO purchases a combination of two year zero coupon bonds and six year zero coupon bonds. Each of these is sold to yield an annual effective yield of 5%. How much of each type of bond should be purchased so that the present value and duration conditions of Redington immunization are satisfied? Is the convexity condition also satisfied at i=5%?