A coupon bond matures in 3 years. Its PAR is $1000 and it makes six coupon payments of $50 semi-annually and assumes that the interests are continuously compounded. Suppose the term structure of the market interest rate is in terms of following forward rate model:
r(t)=0.01-0.002t+0.006t^2-0.0004t^3

What is interest rate term structure in terms of yield curve y(t)?

What is the net present value (NPV) of this coupon bond?

Find the duration of this bond.

What if the term structure is dynamic such as r (t) =0.01×N (μ=0, σ=0.1)-0.002t+0.006t^2-0.0004t^3, redo the calculation of 1, 2, 3. Hint: the net present value is calculated as expected value of discounted payout.