An investor wishes to be sure she has $20 million in 15 months time. At present, 1-year and 2-year zero-coupon bonds are priced to yield 9.7%. The investor sets up a bond portfolio using the duration-matching principle. Three months after setting up the portfolio, the yields on both bonds increase to 10.2% and then remain at that level for a further 12 months. Assume that all months are of equal length, that all bonds have a par value of $100, and that investors may trade any number of bonds, including fractions of bonds. Show that the investor will achieve her target sum. Be precise about the timing and amounts of any transactions required. Show your calculations.