29. Let us revisit a lending-to-a-friend problem we discussed in class. Suppose you are lending $25 dollars to a friend, and, being a nice friend, you will charge her/him only $1 in interest for the convenience (and as a preventive measure against your friend's nascent habit to borrow here and there). The two of you agree that in one week from today your friend repays $10, and in two week from today s/he will pay the remaining $16. (a) Draw a graphical representation of the loan and its repayment schedule with a timeline. Make sure that the outgoing amounts are with a minus sign, while incoming amounts are with a plus sign. (b) Using your diagram in (a), write down the fundamental equation that relates the loan value, pay- ments, and yield to maturity. (c) Find the implied yield to maturity by solving the equation in (b) (feel free to use the same trick we have used in class to expedite and simplify your solution). (d) Convert the found YTM into APR (with four decimal places). (e) Consider the following tweak: your friend first makes $16 payment and then, after two weeks, pays the remaining $10. Will the yield to maturity change or stay the same? (f) Again, set up the equation and solve for the YTM. (g) If the YTM in (d) is equal to the one in (c), explain the reason behind their equality. If, however, they are different, explain whether this makes sense and the reason for the difference