Suppose that the risk-free term structure is given as follows: 

Maturity rate (EAR) 1 Year 2.0% 2 Year 1.8% 3 Year 1.6% 4 Year 1.4% 5 Year 1.2%

(a) Find the present value of a five-year annuity that pays $1 per year (i.e. the security that pays $1 at t = 1, 2, 3, 4 and 5).

(b) Find the 5-year annual swap rate. That is find the coupon rate c for the fixed rate of a five-year swap that exchanges an annual fixed coupon c for an annual floating coupon (coupon at time t is rt1(1 year).). Hint: The answer to (a) will make this easier.

(c) Suppose that you enter into a five-year payer swap with notional value $100M. If rates immediately go up after you enter the swap, is this good news or bad news for you?

(d) Suppose that you enter into a five-year payer swap and immediately afterwards, rates go up 0.10% (parallel shift up). What will the new value of the swap be? You may use the duration/modified duration approximation even though the yield curve is not flat.