A loan of 10000$ is to be repaid with annual payments, at the end of each year, for the next 20 years. For the first 5 years the payments are k per year ; the second 5 years, 2k per year ; the third 5 years, 3k per year ; and the fourth 5 years, 4k per year.

(a) Draw two timelines describing this series of payments.

(b) For each of the timelines in (a), and an expression for k in terms of annuities an.