John seeks to implement a project currently valued at 10000 five years from now. The project cost is subject to inflation, which is expected to follow a continuous rate rt = 0.02 +0.01t if 0 5. (a) If John seeks to finance the project with contributions at the beginning of each year of respectively 5X, 4X, 3X, 2X, and X to a fund earning an effective annual rate of 5%, what is the value of X ? (b) John decides not to implement the project right away after five years, but inflation restarts at a rate of rt = 0.02+0.01t (where t starts from time 5). For how much time will John's fund be sufficient to cover the project fees with no additional payment ? Assume the effective rate stays the same as in part (a)