I understand that the 6 year spot rate shouldn't be below the 5 year one but could someone help me understand how the arbitrage part works?

In order to profit from this mis-pricing, I'm guessing that the $1000 amount borrowed is a random number but how would you know to lend 990?

Many thanks!!

Look at the spot interest shown in question 8. Suppose that someone told you that the six-year spot interest rate was 4.80 percent. Why would you not believe him? How could you make money if he was right? What is the minimum sensible value for the six-year spot rate? A 6-year spot rate of 4.8 percent implies a negative forward rate: To make money, you could borrow $1,000 for 6 year at 4.8 percent and lend $990 for 5 years at 6 percent. The future value of the amount borrowed is: The future value of the amount loaned is This ensures enough money to repay the loan by holding cash over from year 5 to year 6, and provides an immediate $10 inflow. The minimum sensible rate satisfies the condition that the forward rate is 0%: This implies that r6 = 4.976 percent