As a professional financial consultant, you try to advise on the position of a diversified portfolio. Your task is to explain to the management team on the bond sensitivity, which requires you to:

(a) Calculate the duration of a five-year, $3,000 Treasury Bond with a 10 per cent semi-annual coupon selling:

(i) at par?

(ii) selling with a yield to maturity of 20 per cent?

(b) Conclude on the relationship between the duration and yield to maturity based on part (a) results. Justify your answer with support.

(Notes: Please select consistent decimal point for the calculation of PVIFi,n in the financial table.)