Consider the following problem. You lend your friend $10 today, which s/he promises to repay you in two instalments of $5.25 each. The first instalment is to be paid in two weeks from today; and the second—in four weeks from today. Using the information given, please complete these tasks: (a) Sketch a diagram showing cash flows from your perspective as a lender. (b) Set up an equation that relates the cash flows and YTM. (c) Solve the equation by hand. [Hint: If you have set up the equation correctly in part (b), then it is a quadratic one. You are welcome to solve it either by completing a square or via the standard formula for the roots.] (d) Since there are two roots, you should obtain two values for the YTM. What are they? (e) Choose the value that you believe to be correct and offer an argument showing why it is so, using the information given. (f) To what time period does the value of YTM you have chosen in (e) correspond? Annualize your YTM.