Consider a 2-year bond with a principal of $100 that provides coupons at the rate of 3.8% per annum semiannually. Suppose the yield on this bond is 6.1% per annum with continuous compounding.

(a) What is the duration of this bond?

(b) Suppose the yield on this bond increases by 0.1%.

i. Calculate the new bond price exactly.

ii. Estimate the new bond price approximately using duration.