In order to ensure the profitability of company, you are required 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 four-year, $2,000 Treasury Bond with a 8 per cent semiannual coupon selling:

(i) at par?

(ii) selling with a yield to maturity of 15 per cent?

(b) Conclude on the relationship between the duration and yield to maturity based on part (a) results.(Notes: Please select consistent decimal point for the calculation of PVIFi,n in the financial table.)