Suppose that a floating rate bond with a principal of $100 pays coupons every 6 months. The coupon amount is determined by the 6-month LIBOR quoted in the market 6 months before. That is to say,

- the first coupon is the interest accrued for 6 months using todays 6-month LIBOR - the second coupon, one year from now, is the interest accrued for 6 months using the 6-month LIBOR quoted in 6 months - the third coupon, one and a half years from now, is the interest accrued for 6 months using the 6-month LIBOR quoted in 12 months The objective of this exercise is to show that the price of such bonds is always the notional at every coupon date.

(a) Suppose that this is a 6-month bond. What is the price of this bond? (b) Suppose that this is a 1-year bond. What is the price of this bond? Hint: use (a) to argue that you know the price of the bond in 6 months. (c) Suppose that this is a N-year bond. What is the price of this bond? Hint: Generalize (a) and (b) to come up with the wanted result.

Edit: I think this is more of a theoretical question as opposed to numerical calculations. As in, how does the price of the 6 month bond relate to the timings of the coupons and notional values? Etc. Such as in question (c) it tells us to generalize the other answers, as in explain the concepts.