Assume that SOFR rates are risk free. Suppose you have a 10 year note that pays an annual coupon of (10%2 daily compounded SOFR). Such a note is called an inverse floater. Suppose the face value is $100 and a flat rate curve of 5% annually compounded. (a) What is the price of the bond? (Hint: Replicate with floating rate bonds, coupon bonds and zero coupon bonds). (b) What is the modified duration? (Hint: Find price as a function of interest rate, and take the derivative). (c) Compare the modified duration to the maturity. Do you find this surprising