You see the following bonds trading in the market at the following prices. Is there an arbitrageopportunity? If so, tell me how you know that.

One-year zero-coupon bond with a face value of $100 trading for $95.

Two-year zero-coupon bond with a face value of $100 trading for $90.

Three-year zero-coupon bond with a face value of $100 trading for $80.

Three-year annual coupon bond with a face value of $100 and a coupon rate of 5% trading for $100.A: The three-year annual coupon bond with a face value of $100 pays $5 in year 1 and 2, and pays$ 105 in year 3.

It costs you $100.To replicate the cash flow, you can buy the one-year zero-coupon bond with a face value of $5, the two-year zero-coupon bond with a face value of $5 and the three-year zero-coupon bond with a face value of $105.In total, you pay: 0.955 + 0.95 + 0.8105 = 93.25Which is less than the price of the three-year annual coupon bond with a face value of $100.Therefore, you can arbitrage by selling the three-year annual coupon bond with a face value of$100 and buy the replicated bond with three zero-coupon bonds and earn a positive profit.

This is the question and answer, could someone please tell me why you multiply .95x5? Like I get the .95 comes from the 95$ and the 5$ comes from the Three-Year Annual coupon first-year cash flow but why do you do this? Also in the arbitrage setting, which are you buying and which are you selling? How can you only buy a "bond with a face value of $5"? Thank you.